No, both poles are equally strong.
Most other online calculators are based on theoretical formulas, which are notoriously inaccurate, especially for very large or very small sizes. Our fanatical engineers have worked long and hard in the laboratory developing our online calculators that are VERY accurate based on thousands of test cases. Our pull force and magnetic field density calculators can be found here: K&J Magnet Calculator.
Neodymium (more precisely Neodymium-Iron-Boron) magnets are the strongest permanent magnets in the world.
No, we don't, nor does anyone else, because they don't exist. All magnets must have at least two poles.
Yes, two or more magnets stacked together will behave exactly like a single magnet of the combined size. For example, if you stacked two of our 1/8" thick D82 disc magnets to form a 1/4" thick stack, the two magnets would have about the same magnetic strength as the 1/4" thick D84 discs. This is described in more detail in the second half of our article about Doubled Forces.
We use the description "Magnetized thru thickness" to identify the locations of the poles on our block magnets. The thickness is always the last dimension listed for block magnets. If you take one of our block magnets and place it on a flat surface with the thickness dimension as the vertical dimension, the poles will be on the top and bottom of the magnet as it sits. For example: Our BX082 blocks are 1" x 1/2" x 1/8" thick. If you place one of the blocks so it is on a flat surface with 1/8" as the vertical dimension, the poles will be on the top and bottom as the magnet sits. This means the poles are located in the middle of the 1" x 1/2" sides. Click here for Magnetization Directions Illustrated.
Ferromagnetic materials are strongly attracted by a magnetic force. The elements iron (Fe), nickel (Ni), and cobalt (Co) are the most commonly available elements. Steel is ferromagnetic because it is an alloy of iron and other metals.
Magnetic fields cannot be blocked, only redirected. The only materials that will redirect magnetic fields are materials that are ferromagnetic (attracted to magnets), such as iron, steel (which contains iron), cobalt, and nickel. The degree of redirection is proportional to the permeability of the material. The most efficient shielding material is the 80 Nickel family, followed by the 50 Nickel family.
In our limited pull force testing using various steels, we have not found much difference between different types of low carbon steel. Anything in the 1006-1018 range, or even A36 steel, perform very similarly.
It's stainless steel that can vary much more wildly. Some stainless steels aren't ferromagnetic at all. We've written about this more in our blog article, Stainless Steel.
Disc, cylinder, and sphere shapes cannot be manufactured this way. Rings magnetized this way are referred to as, "radially magnetized." While such magnets exist, we are currently not able to supply neodymium ring magnets magnetized this way.
Gaussmeters are used to measure the magnetic field density at the surface of the magnet. This is referred to as the surface field and is measured in gauss (or tesla). Pull Force Testers are used to test the holding force of a magnet that is in contact with a flat steel plate. Pull forces are measured in pounds. Fluxmeters and Helmholtz coils are used to measure the magnetic moment. Learn more in our article about Measuring Magnets.
Because pull force values are tested under laboratory conditions, you probably won't achieve the same holding force under real world conditions. The effective pull force is reduced by uneven contact with the metal surface, pulling in a direction that is not perpendicular to the steel, attaching to metal that is thinner than ideal, surface coatings, and other factors.
Yes, we've posted Demagnetization Curves for our most common Neodymium magnet grades right here.
All of the pull force values we specify have been tested in our laboratory. We test these magnets in several different configurations. Case 1 is the maximum pull force generated between a single magnet and a thick, ground, flat steel plate. Case 2 is the maximum pull force generated with a single magnet sandwiched between two thick, ground, flat steel plates. Case 3 is the maximum pull force generated on a magnet attracted to another magnet of the same type.
The values are an average value for five samples of each magnet. A digital force gauge records the tensile force on the magnet. The plates are pulled apart until the magnet disconnects from one of the plates. The peak value is recorded as the "pull force". If using steel that is thinner, coated, or has an uneven or rusty surface, the effective pull force may be different than recorded in our lab.
The traditional way of visualizing magnetic fields is to place a magnet near a surface covered with iron filings. If you already have some of our magnets, this is a good experiment to conduct! In the meantime, we've created a series of images using Finite Element Analysis software, which can be viewed here.
This is a very interesting question. It's actually a difficult question to answer well. As the late, great physicist Richard Feynman once said, "How much of an explanation is enough to satisfy you?" To watch him describe the difficulty in answering this question, check out Feynman: How do Magnets Work on YouTube.
If you do want more details, this interesting video: How Special Relativity Makes Magnets Work has a great description about why an electromagnet is attracted to iron.
Their follow-on video, MAGNETS: How Do They Work? is even more relevant to permanent magnets. It addresses how permanent magnets with (seemingly) no current running through them can act magnetic. Ironically, even with that incredible level of detail, at some point they still end up saying, "(Why?) No one knows. We just know that's the way the universe works." Feynman was a pretty smart guy!
There are several simple methods that can be used to identify the (Scientific) North and South poles of neodymium magnets.
1) The easiest way is to use another magnet that is already marked. The North pole of the marked magnet will be attracted to the South pole of the unmarked magnet.
2) If you take an even number of magnets and pinch a string in the middle of the stack and dangle the magnets so they can freely rotate on the string, the North pole of the magnets will eventually settle pointing North. This actually contradicts the "opposites attract" rule of magnetism, but the naming convention of the poles is a carry over from the old days when the poles were called the "North-seeking" and "South-seeking" poles. These were shortened over time to the "North" and "South" poles that we know them as.
3) If you have a compass handy, the end of the needle that normally points North will be attracted to the South pole of the neodymium magnet.
4) Use one of our Pole Identifier Devices.
(Please note: In some magnetic therapy applications, the definitions of the poles are reversed from the scientific definition described above. Please be sure to confirm the proper definition of the poles prior to using magnets for medical purposes)
Also check out our article, Which Pole is North?
This depends on a lot of factors, but as a general rule of thumb, we recommend keeping the distance between magnets and electronics 4" + 1" for every 10 lbs of pull force.
While we love answering technical questions about magnets, this one sounds more like a legal question. We're definitely not qualified to provide legal advice.
Again, we are not medical professionals, so we cannot provide firm details on pacemaker issues. As for safety and electronics, it really depends on the application of your product, the size of the magnet(s), how the magnet is used, and where the magnet is located within the product. We recommend providing any warnings that you think may be an issue.
We are not medical professionals, so we cannot offer complete guidance on pacemaker safety, or about any specific medical device. Please consult a physician and/or the manufacturer of your device for this information. We've shared what we do know in our article about Pacemaker Safety.
No, magnets should not harm any of these appliances.
There are no known health concerns with exposure to permanent magnetic fields. In fact, many people believe that magnets can be used to speed up the healing process. There may be issues with people with pacemakers or other implanted medical devices handling or being around strong magnets. We are not medical professionals, so we cannot offer complete guidance on pacemaker safety. We've shared what we do know in our article about Pacemaker Safety. Please consult a physician for this information. There are several safety concerns when handling strong magnets. Please refer to our Safety Page for complete details.
Maybe...The strong magnetic fields of these magnets can damage certain magnetic media such as floppy disks, credit cards, magnetic I.D. cards, cassette tapes, video tapes or other such devices. They can also damage televisions, VCRs, computer monitors and other CRT displays. Never place neodymium magnets near any of these appliances. As for other electronics such as cell phones, iPods, flash drives, calculators and similar devices that do not contain magnetic storage media, probably not, but it is best to err on the safe side and try to avoid close contact between neo magnets and electronics.
Not unless you really work at it. While you probably don't want to stick magnets directly to your computer case, having them nearby will not harm your computer. Magnets can damage floppy disks and magnetic tape storage media, so you must keep magnets away from these items. They should not, however, damage any data on your hard drive unless you place a very large and powerful magnet directly on top of the drive. Every hard drive already contains a powerful neodymium magnet, so one moving around outside the case will not affect the data.
We tried scrambling the contents of a running hard drive ourselves, and documented our failure to erase all the data in our article, Hard Drive Destruction
Using adhesive tape to capture the metal dust is the best way to clean magnets.
Small and medium-sized magnets can usually be separated by hand by sliding the end magnet off of the stack. Medium-large magnets can often be separated by using the edge of a table or countertop. Place the magnets on a table top with one of the magnets hanging over the edge. Then, using your body weight, hold the magnet(s) on the table and push down on the magnet hanging over the edge. With a little work and practice, you should be able to slide the magnets apart. Just be careful that they don't snap back together once they become separated. For very large magnets (generally 2" and larger), we use a specially made magnet separating tool. You can see pictures of one of these tools as well as instructions on how to build your own on this page: Build your own magnet separating tool.
For a more in-depth explanation, check out our article: How to Separate Strong Magnets which includes a number of short videos.
According to the United States Department of Transportation, the Office of Hazardous Materials Safety, and the International Air Transport Association, the upper limit for shipping magnets by air is a magnetic field strength of 0.00525 gauss measured at 15 feet (4.5 meters) from any point on the outside of the package. If you can measure more than 0.00525 gauss at 7 feet away, it may require labeling as a dangerous good / magnetized material. There are no restrictions on the shipping of magnetized materials by ground. When in doubt, ship magnets by ground transportation.
Neodymium magnets are a member of the rare earth magnet family. They are called "rare earth" because neodymium is a member of the "rare earth" elements on the periodic table. Neodymium magnets are the strongest of the rare earth magnets and are the strongest permanent magnets in the world.
Neodymium magnets are actually composed of neodymium, iron and boron (they are also referred to as NIB or NdFeB magnets). The powdered mixture is pressed under great pressure into molds. The material is then sintered (heated under a vacuum), cooled, and then ground or sliced into the desired shape. Coatings are then applied if required. Finally, the blank magnets are magnetized by exposing them to a very powerful magnetic field in excess of 30 KOe.
Learn more in our article about How Neodymium Magnets are Made.
As a general rule of thumb, a peak field of between 2 and 2.5 times the intrinsic coercivity is required to fully saturate a magnet. For standard neodymium magnets, the field required is minimum of 24 KOe, but 30 KOe is usually the minimum used.
Yes, our magnets are fully RoHS compliant, meeting the European Parliament Directive entitled "Restrictions on the use Of Hazardous Substances" (RoHS). This Directive prohibits the use of the following elements in electrical/electronic equipment sold after 7/1/2006: cadmium (Cd), lead (Pb), mercury (Hg), hexavalent chromium (Cr(VI)), polybrominated biphenyls (PBBs) and polybrominated diphenyl ethers (PBDEs). Download an official RoHS Compliance Statement from K&J Magnetics here. Or, you can find individual PDF files for each specific magnet on the product detail pages, under the "Downloads" tab.
No, neodymium magnets do not require a keeper for storage like Alnico magnets.
No, once a magnet is fully magnetized (saturated), it cannot be made any stronger
Here are the dimensions of these coins along with the closest matching magnet that we currently stock:
You definitely cannot solder or weld to neodymium magnets. The heat will demagnetize the magnet and could cause it to catch fire posing a safety risk.
Very little. Neodymium magnets are the strongest and most permanent magnets known to man. If they are not overheated or physically damaged, neodymium magnets will lose less than 1% of their strength over 10 years - not enough for you to notice unless you have very sensitive measuring equipment. They won't even lose their strength if they are held in repelling or attracting positions with other magnets over long periods of time.
The grade, or "N rating" of the magnet refers to the Maximum Energy Product of the material that the magnet is made from. It refers to the maximum strength that the material can be magnetized to. The grade of neodymium magnets is generally measured in units millions of gauss oersted (MGOe). A magnet of grade N42 has a Maximum Energy Product of 42 MGOe. Generally speaking, the higher the grade, the stronger the magnet.
The Neodymium Iron Boron material is very hard and brittle, so machining is difficult at best. The hardness of the material is RC46 on the Rockwell "C" scale, which is harder than commercially available drills and tooling, so these tools will heat up and become damaged if used on NdFeB material. Diamond tooling, EDM (Electrostatic Discharge Machines), and abrasives are the preferred methods for shaping neodymium magnet material. Machining of neodymium magnets should only be done by experienced machinists familiar with the risk and safety issues involved. The heat generated during machining can demagnetize the magnet and could cause it to catch fire posing a safety risk. The dry powder produced while machining is also very flammable and great care must be taken to avoid combustion of this material.
Yes. Neodymium Iron Boron magnets are sensitive to heat. If a magnet heated above its maximum operating temperature (176°F (80°C) for standard N grades) the magnet will permanently lose a fraction of its magnetic strength. If they are heated above their Curie temperature (590°F (310°C) for standard N grades), they will lose all of their magnetic properties. Different grades have different maximum operating and Curie temperatures. See our Neodymium Magnet Specifications Page for more details. Also check out our in-depth article about Temperature and Neodymium Magnets, where we dive into enough technical detail to reveal how this topic is actually a bit more complex. We do stock a range of high temperature magnets, which you can see here.
While we've certainly heard this question before, it's not clear what answer you're looking for. A few different magnet properties are specified in gauss. From our Magnet Grades article:
How many Gauss is a magnet?
We’re often asked if a magnet “has 10,000 Gauss.” This is a bit of a strange question, since Gauss is a unit of magnetism that can apply to different measurements or magnet properties. A magnet doesn't have one specific amount of Gauss in it. Two common measurements expressed in Gauss are The Residual Flux Density, Br, and the Surface Field.
Residual Flux Density, Br, is the magnetic induction remaining in a saturated magnetic material after the magnetizing field has been removed. Scroll down to the last section of this article for a more detailed explanation.
This number is a material property which is independent of the magnet shape. Grade N42 magnets have a Br of 13,200 Gauss, while N52 magnets can be as high as 14,800 Gauss. See our Specs page for more Br values for various neodymium magnet grades.
The Surface Field is the strength of the magnetic field measured right at the surface of the magnet. It’s the field strength you might measure if you could squish a magnetometer’s sensor right up against the surface. This number depends on the magnet material, the shape of the magnet and how it’s used in a magnetic circuit.
In either case, you can find values for each of these properties on the product pages for each of our magnets.
In most applications, the answer is simply "no". If the magnets will be exposed to higher temperatures while in repelling applications, the answer is "possibly". The exact answer is a bit too complicated for a FAQ answer, and requires specifics about the application.
You can download all documentation and certifications, including REACH, Conflict Minerals, MSDS, Certificate of Origin, Certificate of Compliance, and more on the product description page of the specific magnet you are interested in, under the "Downloads" tab.
From a dictionary: [nē ō dim ē um]. Or, nee-oh-dim-ee-um.
The only real trick to pronouncing it correctly is to treat the 'y' as an 'i'. It is pronounced as if it were spelled "neodimium".
The maximum operating temperature is the maximum temperature the magnet may be continuously subjected to with no significant loss of magnetic strength. This is 176°F (80°C) for standard grades of neodymium magnets. The Curie Temperature is the temperature at which the magnet will become completely demagnetized. This is 590°F (310°C) for standard grades of neodymium magnets. Higher temperature grades have higher maximum operating temperatures and higher Curie Temperatures. At temperatures between these two points, a magnet will permanently lose a portion of its magnetic strength. The loss will be greater the closer to the Curie Temperature it is heated.
For a more in-depth explanation, check out our article: Temperature and Neodymium Magnets.
This law requires reporting of the use of columbite-tantalite (tantalum, used in capacitors), cassiterite (used to make tin), wolframite (tungsten) and gold that comes from mines located in the eastern part of the Democratic Republic of Congo. Since neodymium magnets don't usually contain these elements, they shouldn't be covered by this law. Learn more about what elements are used in the manufacture of neodymium magnets in our article: How Neodymium Magnets are Made.
No. All magnets must be shipped in a box to comply with United States Department of Transportation, USPS, and UPS regulations for the shipment of magnetic materials.
We accept Purchase Orders from businesses with approved credit. For additional information, please email us at firstname.lastname@example.org.
You can receive discounts by joining our Mailing List. Our periodic newsletter, sent once a month, contains news, new products and Mailing List exclusive coupons and specials.
You can view all current pricing and price breaks directly on our website. If you need a formal quote for our magnets, you can create a downloadable PDF directly from our website. Simply place the magnet(s) you want into the online shopping cart. Be sure to put in the correct quantity -- the cart automatically includes discounts based on the number you purchase.
Once you've added all the items you want, navigate to https://www.kjmagnetics.com/cart.asp. Beneath the list of items in your cart, you'll find a link to download your PDF quote. It reads something like:
Need a formal quote? Click here to download a PDF quote of items currently in your shopping cart.
We and several customers have had great success adhering to the nickel-plating using Loctite 39205 (an acrylic adhesive) with Loctite 7380 activator. A Loctite representative also recommended Loctite 3032 (a 2-part acrylic adhesive) with Loctite primer 770. For more commonly found adhesives, we have also had great results using many kinds of epoxy, often sold as "5-minute" epoxy. "Liquid Nails" and "Gorilla Glue" can also work well, and are available in most hardware and home supply stores. It does help to scratch the surface of the plating lightly with sandpaper or other abrasive prior to applying the adhesive. For more information, read our in-depth article: Sticky Business: How to Glue Neodymium Magnets.
We have found that wrapping magnets with a few layers of electrical tape protects them from most damage caused by collisions with other magnets and hard surfaces. Another great way to protect your magnets from damage and the elements is to coat them with rubberized coating. We have created a page with step-by-step instructions on how to do this. We also stock several sizes and shapes of plastic-coated and rubber-coated magnets.
Yes, you can use any paint formulated for use on metal surfaces. Spray-on paint seems to work best. Roughing the surface first can help improve paint adhesion to the smooth, nickel plated surface. Sandblasting or beadblasting works, as well as an etching primer. Check out our blog article, Painting Magnets, for some more information.
NdFeB material will oxidize if it is exposed to moisture. For this reason, we do not stock any unplated magnets. We can supply unplated magnets as custom order items.
These materials don't "weaken" the magnet, but the volume of magnet material is reduced to allow room for the coatings, which reduces the pull force. The layer of plastic or rubber also creates distance between the magnet and metal surface which also reduces the pull force.
Choosing different coatings does not affect the magnetic strength or performance of the magnet, except for our Plastic and Rubber Coated Magnets. The preferred coating is dictated by preference or intended application. More detailed specifications can be found on our Specs page.
Maybe. Each of our plastic or rubber coated magnets require its own special mold. A new size requires a new mold, with a one-time cost of $300-$2,500, depending on the size and shape. If you need a large quantity of such magnets, creating a new mold may be worthwhile. If you only need a few, doing your own rubber coating might be more cost effective. Be sure to look through our complete list of Plastic and Rubber Coated Magnets.
Neodymium magnets are composed mainly of Neodymium, Iron, and Boron. If neodymium magnets are not plated, the iron in the material will oxidize very easily if exposed to moisture. Even normal humidity will rust the iron over time. To protect the iron from exposure to moisture, most neodymium magnets are plated or coated.
The nickel plating is actually triple plating of nickel-copper-nickel. The combined thickness totals 15-21μm.
Our main office and warehouse are currently located in Pipersville, PA, about 30 miles north of Philadelphia. We do not have a retail store, nor are we able to accept walk-in customers or pick-ups.
We do not have any local distributors of our magnets. All sales are through our website and ship from our location here in Pennsylvania.
No, we do not have a printed catalog available. Find information about all of our magnets online, here at our website.
Yes, we can supply custom magnets. You can find details on our Custom Magnet page.
A wide range of sizes can be used for magnetic therapy. Many people use magnets as small as our D41 discs for spot treatment, while others use magnets as large as our DY04 discs for large area treatment. It is best to select a size that "fits" the area being treated. To avoid issues with nickel allergies, gold plated magnets like these are often preferred.
Magnets on the main water line should be of dimensions 1.5 - 2.5 times the outside diameter of the pipe coming in. Larger magnets will provide a stronger and more consistent magnetic field between them. For this application, we often recommend our BY0Y08 blocks. They will work well on any water line up to 1.5" in diameter. Water conditioning works best if you use two magnets, one on each side of the pipe in attracting arrangement. The two magnets in this arrangement create the strongest possible magnetic field between them. It works very well if you have two "shims" which are the same thickness as the diameter of the water pipe. If you tape the shims to either side of the pipe, they will provide a flat surface for the magnets to rest on. The large magnets should hold each other in place across the pipe and shims. The magnets can then be held in place with tape to prevent them from slipping off due to vibration.
Interested in learning more about how magnetic water treatment might work? Check out our Magnetic Water Treatment article, where we discover some surprising facts about this controversial subject!
For refrigerator magnets, there are many options. We carry a neat line of magnetic thumbtacks as well as dozens of other shapes and sizes that work well. A few suggestions are our D42, D34, B333, S4 (also available in black color or gold), and ST4 stars. Many other magnets of similar sizes will also work very well for fridge magnets.
Also check out our Refrigerator Magnets section, which includes a number of great suggested magnets.
Dent removal is accomplished by inserting a steel ball into the instrument as close to, but smaller than, the diameter of the section of tubing being repaired. The steel ball can be moved through the tube using a magnet on the outside. Working the steel ball over the damaged area will gradually smooth out the dent. A magnet like our DX0X0 will pull out most small- and medium-sized dents, while a larger magnet like our DX8C may be necessary for larger and more stubborn dents. We do carry a line of steel balls that can be used for this application.
For holding average-sized pins and badges, we recommend our D62 disc magnets, as they provide the appropriate amount of pull strength through a wide range of fabric thicknesses. If you will be holding large or heavy pins or badges, or will be holding through exceptionally thick material, then our D72 or D82 discs may be necessary to provide enough holding force.
Also check out our Sewing Magnets that are made specifically for use as magnetic closures. They are intended to be sewn inside the fabric, remaining hidden from view.
They come in 3 different sizes and are sold in matched pairs. Also note that some have a thin plastic cover that protects them from moisture, which is an excellent solution for anything that goes through the washing machine.
See our Sewing Magnet Article for an example of how to use them. There, we describe how we replaced the Velcro fasteners on a pair of cargo shorts.
We have many printers and other customers that use our magnets in brochures and binders to hold them closed. The most common sizes used for brochures and binders are our D401, D41, D501, D51, D601, D61, D701, D71, D801, D81 disc magnets, and our B4401, B441, B6301, B631, B661, B821, B841, B8801, and B881 block magnets, but larger sizes can also be used for larger applications.
See our Adhesive Backed Magnets article for a great example of how to do this.
No, we specialize in sintered neodymium magnets. These are solid, brittle blocks - not like the flexible magnets you might see a business card printed on. We do not sell those kinds of magnetic sheets.
The magician's M5 (aka PK5) magnet is the equivalent of our BY0Y08 block magnet.
Some customers use neodymium magnets to create earrings that clamp over the earlobe, not requiring a piercing. Small discs can work this way, but avoid magnets that are too large. We find that anything much stronger than a pair of D21 disc magnets might be a little too strong -- left on too long, larger magnets can start to hurt. Experiment with a few sizes, especially magnets with a listed pull force less than 0.5 lb. Examples include D201, D201-N52, D21, D21B-N52, D301, and D301-N52.
People with a nickel allergy should avoid long exposure of nickel plated magnets against their skin.
Magnetic tapes can be erased with a strong magnet. Popular choices include: DX8C, DY0X0, or BY0Y08.
We used to think that a sufficiently large magnet would scramble the data on a hard drive. Some recent experiments we have conducted seem to disagree. See our blog article on the subject for more details. We don't recommend this method if you must be sure that the data is gone -- physical destruction of the drive is the safest choice.
The answer varies depending on the size of the can and the weight of the items being stored. Magnets as small as our D81 discs can be used to hold smaller cans, while magnets as large as our DC2 discs may be required to hold very large cans. Check out our Magnetic Spice Jars article to see our experiences adding magnets to popular glass jars.
This one is a definite "maybe". We have received feedback that magnets as small as our D84 discs have successfully triggered traffic lights, but we have also received reports that magnets as large as our DX8C have failed to trip similar traffic light sensors. It seems that there are different types and different sensitivities of traffic light sensors, and magnets will trigger some, but not all of them. If you have any feedback or good information on this, we would appreciate an email with any details you may have.
We have heard from many customers who use our strong magnets to hold up sunscreens to the windscreen of an RV.
How strong do you need the hold to be? Obviously, this involves many factors, from the size and shape of the shade, to how strong a windstorm you expect to withstand. The key is the thickness of the windshield. A pair of magnets will attract towards each other, but the strength drops quickly as you move the magnets farther apart.
We've heard from a number of people who have made their own, using DC6 magnets inside and waterproof DC6PC-BLK magnets outside.
Some commercial products use magnets as large as our 1" diameter DX06 discs.
While this technically is possible, we think in most cases it's not a great idea to try re-magnetizing a fridge seal with a neodymium magnet. A lot of times problems with fridge seals come from the seal being dirty or deformed in some way, not because the magnet got weaker over time. Rubbing a neodymium magnet over your fridge seal can either demagnetize the seal completely or weaken it, and end up making the problem worse.
We discuss this in greater detail in our blog, check out Re-Magnetizing Refrigerator Seals for a more detailed explanation.