Magnetic Flux Density Calculator

Magnetic flux density is one of the most commonly used values for evaluating the magnetic performance of finished magnets at a defined position. Also known as magnetic induction or the B field, it may be measured on magnet surfaces or at a defined distance and is normally expressed in tesla or Gauss. Magnetic flux density measured at magnet surfaces is commonly referred to as surface field.

Although magnetic flux density is sometimes described as magnet strength or misleadingly referred to as magnetic field strength, these terms are not equivalent. Magnetic flux density is different from magnetic field strength, pull force, magnetic moment, and the intrinsic magnetic properties of magnet materials.

For regular-shaped magnets, magnetic flux density at a defined position can be estimated from remanence, magnet dimensions, magnetization direction, and distance from the pole surface. The calculators below estimate magnetic flux density along the centerline of axially magnetized cylinder and block magnets under simplified conditions.

Magnetic Flux Density Calculator for Cylinder Shape

Magnetic Flux Density Calculator for Block Shape

Calculation Notes and Limitations

Calculation Notes:

These calculators use analytical magnetic field equations for uniformly magnetized cylinder and block magnets with regular geometry. They are applicable to axially magnetized Neodymium magnets, Samarium Cobalt magnets, and ferrite magnets.
The calculations assume ideal magnet dimensions and pole surfaces. Coatings, chamfers, dimensional tolerances, nonuniform magnetization, and surrounding magnetic components are not included.
Distance should be measured from the magnetic pole surface to the calculation point. When comparing calculated results with Hall probe measurements, coating thickness, sensor encapsulation, fixture clearance, and the position of the Hall sensing element should all be considered.
Magnetic flux density decreases as the distance from magnet surfaces increases. Even a small unaccounted gap can therefore produce a noticeable difference between calculated and measured values.
Calculation results are preliminary estimates. Magnetic flux density describes the magnetic field at a defined position and should not be used alone to represent the overall magnetic performance of finished magnets. Magnetic flux or magnetic moment may be more suitable for comparing total magnetic output.

Why Ring Magnets Are Not Included

Magnetic flux density of axially magnetized ring magnets can also be calculated analytically by considering the difference between the outer and inner cylindrical geometries. However, ring magnets are not included in these online calculators because the measurement position is more difficult to define and reproduce consistently in practice.

Hall probes must be accurately aligned with the centerline of ring magnets, while the measurement position may be defined at the pole surface, within the central opening, or at a specified distance above magnet surfaces. Small changes in probe position, orientation, or distance can produce noticeably different readings, particularly near the inner diameter.

For this reason, a simplified ring magnet calculator may provide a numerical result without offering the same practical value or measurement comparability as the cylinder and block calculators.

How to Interpret the Calculated Result?

The calculated value represents magnetic flux density at a specific point on the centerline extending outward from the center of the magnetized pole surface. It is based on the entered remanence, magnet dimensions, and distance from the pole surface. This is a local magnetic field value expressed in tesla or Gauss, rather than a measure of the total magnetic output of finished magnets.

Remanence, Br, is a magnetic material property defined as the magnetic flux density remaining at zero applied magnetic field after the material has been saturated. It is determined from the demagnetization curve under closed magnetic circuit measurement conditions. The calculator instead estimates magnetic flux density at or above magnet pole surfaces under open magnetic circuit conditions. Because magnet geometry produces a demagnetizing field and magnetic flux also leaks through the surrounding space, the calculated value is normally lower than the remanence of the material.

Calculated values are most useful for comparing designs under the same conditions. Magnet shape, measurement position, distance, temperature, and surrounding components should remain consistent when comparing different dimensions or materials. Magnetic flux density cannot be directly converted into pull force and should not be used alone to compare the overall magnetic performance of magnets.

How to Measure Magnetic Flux Density?

Magnetic flux density around magnets in an open magnetic circuit can be measured using a Gauss meter and Hall probe. The reading corresponds to the magnetic flux density at the position of the Hall sensing element, rather than the overall magnetic output of finished magnets.

To compare measured values with calculator results, the Hall sensing element should be positioned on the centerline extending from the center of the magnetized pole surface. The probe must also be oriented to measure the magnetic field component along the magnetization direction. Measurement distance should be defined from the pole surface to the Hall sensing element. Coating thickness, probe encapsulation, fixture clearance, and other intervening gaps should all be taken into account.

Magnetic flux density can change rapidly near magnet surfaces. Small variations in probe position, angle, or distance may therefore produce noticeable differences in measured values. Operator technique, Hall probe type, instrument calibration, fixture design, and measurement procedure can all affect repeatability.

Non-magnetic fixtures can improve positioning consistency. Comparative measurements should use the same calibrated Gauss meter, Hall probe, fixture, temperature, reference position, and test procedure for all samples.

Why Calculated and Measured Values May Differ?

Differences may remain even when the instrument, probe positioning, operator technique, and measurement procedure are carefully controlled. The calculator is based on entered material data, idealized geometry, uniform magnetization, and isolated magnetic circuit conditions, while actual magnets and their operating environments may differ from these assumptions.

Remanence can vary within the specified range of each magnet grade. Incomplete magnetization, nonuniform magnetization, or irreversible demagnetization can also reduce measured magnetic flux density compared with calculations based on nominal material data.

Temperature affects the magnetic output of permanent magnet materials. Values calculated from room-temperature material data may therefore differ from measurements taken at other temperatures, particularly for materials with larger reversible temperature coefficients.

Actual geometry may differ from the simplified cylinder and block shapes used in the calculation. Dimensional tolerances, chamfers, edge radii, and coatings can change the effective geometry, the distance to the magnetic material, and the local magnetic field distribution.

The calculator also treats magnets as isolated components. Nearby magnetic materials, return paths, housings, mating components, and other magnets can redirect or concentrate magnetic flux. Calculated and measured values should therefore be compared only when material properties, geometry, temperature, measurement conditions, and surrounding magnetic circuits are clearly defined.

When Analytical Calculation Is Not Enough?

These calculators are intended for regular-shaped, axially magnetized cylinder and block magnets evaluated along the centerline of the magnetized pole surface. They are useful for preliminary estimates and design comparisons under simplified conditions.

Analytical calculation becomes less reliable when designs involve off-axis measurement points, complex geometries, multipole magnetization, magnet arrays, nearby magnetic components, magnetic return paths, or several magnets interacting within the same assembly. These conditions can produce magnetic field distributions that are not represented by a simplified centerline equation.

Finite element analysis may be more suitable when magnetic flux density must be evaluated throughout a defined area or volume, or when surrounding components and complete magnetic circuits need to be included. Final designs should still be verified through measurement under actual assembly and operating conditions.

Need help evaluating magnetic flux density in a more complex geometry, magnetic circuit, or assembly? Contact us to discuss your magnet dimensions, materials, measurement position, and operating conditions.