Magnetic Pull Force Calculator: How to Use It

This calculator estimates the pull force between a permanent magnet and a flat ferromagnetic surface (like a steel plate). You enter the magnet’s surface field strength, its pole area, and the air gap distance, and you get the approximate force in newtons and kilograms-force. It uses the standard magnetic circuit approximation, which is accurate for small gaps and simple geometries.

Formula

The calculator uses the magnetic force equation derived from the energy in the air gap:

F = (B² × A) / (2 × μ₀) × (1 / (1 + g/d))²

Where:

• F = pull force in newtons (N)
• B = surface magnetic flux density in tesla (T) – you enter it in millitesla (mT), and the calculator converts it
• A = pole face area in square meters (m²) – you enter it in cm², and the calculator converts it
• μ₀ = permeability of free space = 4Ï€ × 10â�»â�· H/m ≈ 1.2566 × 10â�»â�¶ H/m
• g = air gap in millimeters (mm) – the distance between the magnet face and the steel surface
• d = a characteristic length, taken here as 1 mm (this is a simplification; see limits below)

The first factor (B²A/(2μ₀)) is the force when the magnet is in direct contact (zero gap). The second factor reduces that force as the gap increases. The calculator uses a gap correction of 1/(1+g/10)² where g is in mm, which approximates the drop-off for a typical magnet with a 10 mm thickness. This is an empirical correction, not a universal law.

Worked Example

Using the default values: B = 400 mT, A = 10 cm², g = 0 mm.

1. Convert B to tesla: 400 mT = 0.4 T
2. Convert A to m²: 10 cm² = 10 × 10�� m² = 0.001 m²
3. Gap factor: g = 0, so (1/(1+0))² = 1
4. Force = (0.4² × 0.001) / (2 × 1.2566 × 10��) = (0.16 × 0.001) / (2.5132 × 10��) = 0.00016 / 2.5132e-6 ≈ 63.66 N
5. Convert to kg-f: 63.66 / 9.80665 ≈ 6.49 kg-f

The calculator shows 63.7 N and 6.49 kg-f for the defaults. That means a magnet with a 400 mT surface field and a 10 cm² pole face can hold about 6.5 kg against a flat steel plate when in direct contact.

When to Use This Calculator

This tool is for estimating the holding force of a permanent magnet against a flat, clean, ferromagnetic surface (e.g., mild steel). Use it when:

• You are designing a magnetic latch, clamp, or fixture.
• You want to compare two magnets of different sizes or grades.
• You need to know if a magnet can support a given weight with a safety margin.
• You are estimating the force at a small gap (e.g., through a thin coating or plastic sheet).

It is not for magnets attracting other magnets (the force is roughly double), nor for curved or angled surfaces, nor for very thick gaps (over about 5 mm for small magnets).

How to Read the Result

The result is the maximum static force required to pull the magnet straight off the surface (perpendicular pull). In practice, the force you feel is often lower because:

• Real steel is not perfectly flat or clean – rust, paint, and oil reduce contact.
• Sliding the magnet sideways takes much less force (shear force).
• If the magnet is not fully seated, the air gap reduces the force dramatically.
• Thin steel (less than about 3 mm) can saturate, reducing the effective force.

Always apply a safety factor of 2 to 3 if the magnet is holding something that must not fall. For example, if you need to hold 2 kg, choose a magnet rated for at least 4–6 kg.

Common Mistakes and Limits

• Unit mix-ups: The formula requires B in tesla and A in m². If you enter B in gauss or A in in², the result will be off by orders of magnitude. The calculator handles mT and cm², but if you have gauss, divide by 10,000 to get tesla; if you have in², multiply by 6.4516 to get cm².
• Using the wrong area: For a bar magnet, the pole area is the face that touches the steel. For a horseshoe magnet, it is the total of both poles. For a disc magnet, it is the flat circular face.
• Gap correction is approximate: The 1/(1+g/10)² factor is a rough model. Real force vs. gap curves depend on magnet thickness and shape. For a thin magnet (2 mm thick), the force drops much faster; for a thick one (20 mm), it drops slower. If you need precise values, measure with a force gauge.
• Not for non-ferromagnetic materials: Aluminum, copper, brass, and stainless steel (300 series) are not attracted to magnets. This calculator assumes a ferromagnetic target.
• Temperature effects: Neodymium magnets lose strength at high temperatures (above ~80°C for standard grades). The formula assumes room temperature.

Practical Examples

Here are a few typical scenarios to show how the numbers change:

• Small disc magnet: B = 300 mT, A = 1 cm², gap = 0 → F ≈ 3.6 N (0.36 kg-f). That is a typical fridge magnet.
• Large neodymium block: B = 500 mT, A = 25 cm², gap = 0 → F ≈ 248 N (25.3 kg-f). Enough to hold a small toolbox.
• With a 1 mm plastic coating: Same large magnet, gap = 1 mm → F ≈ 248 × (1/1.1)² ≈ 205 N (20.9 kg-f). A thin layer costs about 17% of the force.
• With a 5 mm gap: Same large magnet, gap = 5 mm → F ≈ 248 × (1/1.5)² ≈ 110 N (11.2 kg-f). The force halves with just 5 mm of air.

Safety and Handling

Strong magnets (above about 5 kg pull force) can pinch skin and cause serious injuries. Always wear gloves and eye protection when handling them. Keep magnets away from pacemakers, credit cards, and electronic devices. Large neodymium magnets can shatter if they snap together – they may chip and send sharp fragments flying. If you are shipping magnets, follow postal regulations for magnetic materials. Never swallow magnets; if two are ingested, they can cause intestinal perforation.

Frequently Asked Questions

What is the difference between pull force and holding force?

They are often used interchangeably. Pull force is the force needed to detach a magnet from a ferromagnetic surface in a perpendicular direction. Holding force is the same thing, usually measured with a force gauge. Some manufacturers rate “holding force� with a thick steel plate (e.g., 10 mm) to maximize the number; others use thinner plate, which gives lower numbers.

Why does my magnet feel weaker than the calculator says?

The calculator assumes ideal conditions: perfectly flat, clean, thick steel. Real surfaces have micro-roughness, paint, or rust that creates tiny air gaps. Also, if the steel is thinner than the magnet’s reach (typically less than 3 mm), it saturates and reduces the force. Finally, the grade of the magnet matters – a N35 magnet has lower B than a N52 of the same size.

Can I use this for two magnets attracting each other?

No. When two identical magnets attract, the force is roughly double the force of one magnet against steel, but the exact factor depends on geometry. For two disc magnets face-to-face, it is about 2×; for two bar magnets side-by-side, it can be different. This calculator is for magnet-to-steel only.

How do I find the surface field (B) of my magnet?

You can measure it with a gaussmeter (teslameter) at the center of the pole face. If you don’t have one, use the manufacturer’s datasheet – most magnet suppliers list the surface field (Br is the residual induction, but surface field is lower). For a rough estimate, a standard neodymium N42 disc has a surface field of about 300–400 mT depending on size.

What if my magnet is not a simple disc or block?

For rings, arcs, or multi-pole magnets, the pole area is not a single flat face. Use the total area of the poles that contact the steel. For a ring magnet, that is the annular face area (π(R²−r²)). For a horseshoe, it is the sum of both pole faces. The formula still gives a rough estimate, but for complex shapes, finite-element simulation is more accurate.

Does the thickness of the steel plate matter?

Yes. If the steel is thinner than the magnet’s magnetic circuit can support, the steel saturates and the force drops. As a rule of thumb, the steel should be at least as thick as the magnet’s thickness for full force. For a 5 mm thick magnet, use at least 5 mm steel. Thinner steel reduces the force, but the exact reduction depends on the magnet’s strength and area.

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in B | Surface field (B) | mT | 400 | 0
in A | Pole area (A) | cm² | 10 | 0
in g | Air gap (g) | mm | 0 | 0
out F | Pull force | N | (B/1000)^2 * (A/10000) / (2 * 1.25663706212e-6) * (1/(1+g/10))^2 | 1
out Fkg | Pull force | kg-f | F / 9.80665 | 2