Calculate magnetic flux through a surface, Φ = B·A·cosθ, from the field strength, area, and angle — or solve backward for the field, area, or angle you need.
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.
Calculate Area from Geometry
° (degrees)
Quick scenarios:
Magnetic flux (Φ)
—
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.
Solve for a different variable
Give the calculator the target flux and the known variables — it solves for whichever one you leave for last.
Solve for
Field strength (B)
—
Enter the target flux and the known variables.
Pick which variable to solve for, then fill in the rest.
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.
Faraday's Law of Induction
Calculate the induced voltage (EMF, $\mathcal{E}$) caused by a changing magnetic flux over time interval $\Delta t$: $\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}$.
Induced EMF / Voltage (ℰ)
—
Enter flux change and time interval to compute induced EMF.
ℰ = -N · (ΔΦ / Δt)Induced EMF
Faraday's Law specifies that induced voltage is proportional to the rate of change of magnetic flux.
2 min read3 steps6 terms3 examples6 FAQsΦ = N · B · A · cosθ
Magnetic flux measures the total magnetic field passing through a surface.
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.
2
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.
3
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.
⚡
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.
✓
General reference
Trust, Methodology & Sources
· Updated July 2026▸
Editorial accountability
Last verified: July 2026
Methodology
Limitations & guidance
Professional guidance:
Primary sources
📖
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.
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.
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.
❓
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?+