Field, area, and angle

Calculate magnetic flux $\Phi = N \cdot B \cdot A \cdot \cos\theta$. Select your preferred engineering units and reference angle mode.

Field strength, B

Area, A

Number of turns, N

Angle

° (degrees)

Quick scenarios:

Magnetic flux (Φ)

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Enter the field, area, and angle to see the flux.

Φ = N · B · A · cosθMagnetic flux

Enter the field, area, and angle to see the magnetic flux.

How the angle scales flux

Uses the field, area, and turns from the Flux tab. Flux scales with $\cos\theta$ — it is maximum at $0^\circ$ and drops to zero at $90^\circ$.

Angle θ	cosθ	Flux Φ	% of Max

Adjust field, area, or turns on the Flux tab to reshape this table.

2 min read 3 steps 6 terms 3 examples 6 FAQs Φ = N · B · A · cosθ

Magnetic flux measures the total magnetic field passing through a surface.

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Walk-through

How to Use This Calculator

3 steps

Enter the field, area, and angle

On the Flux tab, enter the magnetic field strength B (in tesla, mT, µT, or Gauss), surface area A (m², cm², mm², or in²), coil turns N, and angle θ between the field and the surface normal. The calculator updates instantly.

Read the flux & vector diagram

The result card shows total magnetic flux Φ in webers (Wb), computed as Φ = N·B·A·cosθ. The live interactive SVG diagram displays field line alignment and surface normal orientation in real time.

Solve backward or calculate induced EMF

Use the Solve tab to find field, area, turns, or angle for a target flux. Switch to the Induced EMF tab to calculate voltage generated by flux variations over time via Faraday's Law.

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Reference

Formula & Methodology

3 formulas

Magnetic flux linkage

Φ = N · B · A · cosθ

Φ is magnetic flux in webers (Wb), N is the number of coil turns, B is field strength in tesla (T), A is area in m², and θ is the angle between the magnetic field vector and the surface normal. When measuring angle α from the surface plane, θ = 90° − α and Φ = N·B·A·sinα.

Solving backward

B = Φ / (N · A · cosθ) · A = Φ / (N · B · cosθ) · θ = cos⁻¹(Φ / (N · B · A)) · N = Φ / (B · A · cosθ)

Any single variable can be isolated algebraically. Inverse angle calculations clamp floating-point domain bounds to [-1, 1] to ensure mathematical stability.

Faraday's Law of Induction

ℰ = -N · (ΔΦ / Δt)

ℰ is induced electromotive force (voltage) in volts (V), N is the number of loops, and ΔΦ/Δt is the time rate of change of magnetic flux.

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General reference

Trust, Methodology & Sources

· Updated July 2026

Editorial accountability

Last verified: July 2026

Methodology

Limitations & guidance

Professional guidance:

Primary sources

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Glossary

Key Terms Explained

6 terms

Magnetic flux (Φ) A measure of the total magnetic field passing through a surface, equal to field strength times area times cosine of angle from surface normal. Measured in webers (Wb).

Weber (Wb) The SI unit of magnetic flux. One weber equals one tesla times one square meter — the flux through a 1 m² surface perpendicular to a 1 T field.

Flux density (B) The magnetic field strength, measured in tesla (T) or Gauss (G, where 1 T = 10,000 G).

Area (A) The surface area through which magnetic field lines pass, measured in m², cm², mm², or in².

Angle (θ vs α) θ is measured from the surface normal (0° = perpendicular). α is measured from the surface plane (90° = perpendicular).

Faraday's Law (ℰ) The fundamental principle stating that a changing magnetic flux induces an electromotive force (voltage) in a closed circuit.

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Scenarios

Real-World Examples

3 worked examples

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Physics student

Field perpendicular to a coil face

Field strength (B) 0.5 T Area (A) 0.01 m² Angle (θ) 0° Turns (N) 1

With the field pointing straight through the surface (θ = 0°, cosθ = 1), the flux is Φ = 0.5 × 0.01 × 1 = 0.005 Wb — the maximum possible flux for this field and area.

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Lab technician

Multi-turn inductor coil

Field strength (B) 1.25 T Area (A) 100 cm² Angle (θ) 0° Turns (N) 50

With N = 50 turns and A = 0.01 m², total flux linkage is Φ = 50 × 1.25 × 0.01 × 1 = 0.625 Wb.

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Electrical engineer

Induced voltage in a transformer loop

Flux change (ΔΦ) 0.05 Wb Time (Δt) 0.01 s Turns (N) 100

Using Faraday's Law, ℰ = -100 × (0.05 / 0.01) = -500 V induced electromotive force.

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Deep Dive

Understanding Magnetic Flux & Faraday's Law

3 chapters · 2 min read

Magnetic flux measures the total magnetic field passing through a surface. It drives electromagnetic induction — the operating foundation behind transformers, electric motors, and generators.

How the Magnetic Flux Calculator works

Magnetic flux is defined as Φ = N·B·A·cosθ. The cosine term accounts for field direction: only the perpendicular component of magnetic field passing through the surface contributes to flux.

Units and Conversions

Field strength is measured in Tesla (T) or Gauss (G, where 1 T = 10,000 G). Flux is measured in Webers (Wb) or Maxwells (Mx, where 1 Wb = 10⁸ Mx).

Faraday's Law of Electromagnetic Induction

When magnetic flux through a coil changes over time (ΔΦ/Δt), an electromotive force (voltage ℰ) is induced according to ℰ = -N(ΔΦ/Δt). This principle generates virtually all grid electricity worldwide.

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Questions

Frequently Asked Questions

6 questions

What is the formula for magnetic flux?+

Φ = N·B·A·cosθ, where Φ is flux in webers (Wb), N is turns, B is field strength in tesla (T), A is area in m², and θ is angle from the surface normal.

What is the difference between normal angle (θ) and surface angle (α)?+

Normal angle θ is measured from the line perpendicular to the surface (0° = perpendicular field). Surface angle α is measured from the flat surface plane itself (90° = perpendicular field). The relationship is θ = 90° − α.

When is magnetic flux zero?+

Flux is zero when the magnetic field runs parallel to the surface (θ = 90°, cosθ = 0), grazing along it without penetrating.

How do coil turns (N) affect magnetic flux?+

Each turn encloses magnetic flux. Total flux linkage scales linearly with turn count N (Φ_total = N × Φ_single).

What is the unit conversion between Weber and Maxwell?+

1 Weber (Wb) = 10^8 Maxwells (Mx). 1 Tesla (T) = 10,000 Gauss (G).

How does magnetic flux connect to Faraday's Law?+

Faraday's Law states that induced voltage (EMF, ℰ) is produced whenever magnetic flux changes over time: ℰ = -N(ΔΦ/Δt).

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Magnetic Flux Calculator