How to Calculate a Core Area

Core area can be calculated relatively accurately in toroidal shaped magnets using this equation.
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Things You'll Need

  • Magnetic coil with iron core
  • Measuring tape
  • Calculator

Core area refers to the cross-sectional area of a iron core coil used in the fields of magnetism and electronics (also known as electromagnetism). You can calculate the reluctance of the iron core present inside a magnet if you know the length, area and permeability of the iron and surrounding air. In their informative chapter on the subject of magnetism, Science Toys explains that the reluctance reduces as the cross-sectional area increases. This is a valuable point to remember when performing the calculation.

    For a toroid (two-coiled) structure, where the limbs are side by side, the area can be measured simply as the product of the core height and the difference between the major and minor radii. The equation you will need to use is: A = L x W. This answer will be in millimeters squared, and effective core area is always reported in millimeters squared (mm^2), so you have no factor conversion to make here.

    The calculation becomes slightly more complicated when you consider the flux density, and its ability to concentrate where the path length is shortest. To take this into account, you will need to expand the previous equation into the following form, and insert your particular values, depending on your set-up. A = flux density / flux area (B); so, A = h x ln^2 (R2/R1) / (1/R1-1/R2). The answer given will be in meters squared. Don't forget to multiply by 1000 to achieve the standard unit, the mm, for area in these calculations.

    If you don't know your flux density, you can find it easily, by dividing the total flux by the cross-sectional area of the part of your set-up though which the flux flows. This area is calculated, also very simply, by the A = π x r2.


    • The effective area of the core represents the cross-sectional area of one of its limbs, as explained by Surrey University. This usually correlates with the physical or actual dimensions, but can be affected by flux distribution. In practice, the effective core area always depends on the actual core area and the type of materials used in the transformer, such as E-1 laminations. This is then modified by what is called the stacking factor which depends on how the laminations are connected (interleaving or abutting), and also depends on the lamination or core tape thickness. The thinner the material you are using, the closer the effective core area will be to the value of your actual core area.


    • Ensure you take into account the different factors involved in the calculations. For example, the A = L x W equation results in a core area value in millimeters squared, not centimeters squared, so you will need to divide your answer by 10 to get the standard unit.

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