Free calculators for coil and WPT design.
Mutual inductance and coupling from real coil geometry, circular and square Helmholtz pairs, resonant capacitors and link efficiency. Free to use, instant, in your browser.
Mutual inductance calculator
M between two circular or square coils from turns, size, axial gap and lateral offset — or from k, L1 and L2.
Open calculator →CouplingCoupling coefficient calculator
k from coil geometry (with both self-inductances) or from L1, L2 and M, plus a k-versus-gap curve.
Open calculator →FieldHelmholtz coil calculator
Centre field, required current and optimal spacing for circular and square Helmholtz pairs, with axial uniformity.
Open calculator →FieldSquare Helmholtz coil calculator
Square pairs at the 0.5445·a spacing: centre field, current for a target field and the uniform region.
Open calculator →CircuitWPT compensation capacitor calculator
Series–series and series–parallel resonant capacitors from L1, L2, M and frequency, with capacitor voltage stress.
Open calculator →CircuitWPT efficiency calculator
Maximum link efficiency and figure of merit U = k√(Q1Q2), the optimal load and the k needed for a target η.
Open calculator →Built on the same physics as AirInduct Sim
Every calculator uses closed-form or exactly integrated electromagnetics — Maxwell’s formula with elliptic integrals, the Neumann integral and the Biot–Savart law — the same first-principles approach as the AirInduct Sim solver. Each page shows its formulas, assumptions and a worked example, so you can check the numbers by hand.
When one number is not enough — spiral windings, misalignment sweeps, 3D field maps, matching networks or an optimizer — move to the full simulator or read about its features.
Frequently asked questions
Are these calculators free?
Yes. All six calculators are free to use, run their calculations entirely in your browser and need no account.
How are these different from other online coil calculators?
Most online mutual inductance and coupling calculators only rearrange M = k√(L1·L2), so you need k before you start. These compute M and k from the coil geometry itself — shape, turns, size, gap and lateral misalignment — using Maxwell’s elliptic-integral formula and the exact Neumann integral. They also cover square Helmholtz pairs and SP compensation, which most tools skip or get wrong.
How accurate are the results?
For the stated model (thin filament coils in air) the mutual inductance and field results are exact to machine precision or converged to better than one part in a million, and each page lists its assumptions. Real coils add winding width, spiral layout, nearby metal and frequency effects; the full AirInduct Sim simulator handles those.
Can I use the results in a paper or design review?
Yes. Each page shows the formulas, assumptions and a worked example so the numbers can be checked by hand. Cite the underlying formulas (Maxwell, Neumann, Biot–Savart) and state the filament-coil assumption.