Inductance Calculator
A coil's electrical inertia: L = μ₀N²A/l for your own solenoid, the turns-squared lever shown live, and the banked energy that kicks when the circuit opens.
Inductance Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Long air-core solenoid — no end corrections
- No core permeability — vacuum μ₀ only
In short: An air-core solenoid — 500 turns, 10 cm² of section, 20 cm long: L = μ₀N²A/l = 1.570796 mH (with μ₀ = 4π×10⁻⁷ H/m, quoted as the traditional value). The turns card shows the coil's best lever: double N to 1,000 and L SQUARES to 6.283185 mH — four times, because every turn's field threads every other turn. At 2 A the coil banks E = ½LI² = 3.141593 mJ, and that bank explains the flyback kick: open the switch and the collapsing field drives whatever voltage it takes to keep the current moving — V = L·di/dt, the switch's problem, not the law's.
Formula
L = μ₀·N²·A / l · E = ½LI² · μ₀ = 4π×10⁻⁷ H/m · back-EMF: V = L·di/dt
Inductance is electrical inertia: a coil resists CHANGES in current the way mass resists changes in speed, and for a solenoid the rating is geometry — turns squared, section, over length. The squared turns are not a typo: each extra turn both makes more field AND threads more of it. The energy bank is the flyback kick's budget, and it is why coils get snubber diodes.
Worked Example
- Count the turns and enter the coil's section and length.
- Read L — the coil's inertia in henrys.
- Watch the turns-squared lever: double N, quadruple L.
- Enter a current to price the bank the switch will have to absorb.
Defaults: 1.570796 mH; double turns → 6.283185 mH (4×); at 2 A the bank is 3.141593 mJ.
Strengths & Limits Of This Model
Where this engine is strong
- Turns-squared lever computed live
- Flyback bank priced before it kicks
Where it stops
- No ferrite or iron core factors
- No skin effect or self-capacitance
Practical Use Cases
Coil winding
size chokes and pickups
Flyback design
know the bank before it kicks
Teaching
inertia, in its electrical costume
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Inductance Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why do the turns enter SQUARED?
Because each turn plays both roles: it MAKES flux in proportion to its current, and it THREADS the flux every turn makes. Double the turns and you double the making and the threading both — four times the linkage, four times the inductance. The card computes the square from your own N so the lever is visible.
What is mu-naught doing in the formula?
It is the vacuum's exchange rate between current and field — 4π×10⁻⁷ H/m, the value every air-core coil inherits. (Since the SI redefined the ampere it is technically a measured constant, about 1.256637062e-6, but it agrees with 4π×10⁻⁷ to eight digits.) Iron cores multiply it by factors of hundreds to thousands — which is why iron-core chokes are small.
Why does opening the switch kick?
The coil's law is V = L·di/dt: current cannot stop instantly without an infinite voltage, so the collapsing field drives whatever the gap allows — an arc at the contacts, a destroyed transistor, or, if you planned ahead, a snubber diode that catches it. The energy card is the size of that kick.
How is inertia a useful picture here?
Mass resists changes in VELOCITY and banks ½mv²; inductance resists changes in CURRENT and banks ½LI². The analogy is exact enough to design with: LC circuits ring like spring-mass systems, and the resonance formulas fall straight out of the translation.
Why does a longer coil have LESS inductance?
Because the same turns spread over more length make a diluted field — B inside a solenoid falls as the turns-per-metre falls. Short and densely wound beats long and sparse; the formula divides by l to say so.
When does the solenoid formula stop being honest?
When the coil is short and fat: the formula assumes length much greater than section so end effects vanish. For stubby coils the true inductance runs lower; engineers apply correction factors. Enter honest geometry and the page stays honest.
Does the wire's resistance matter here?
For L, no — inductance is pure geometry (and the core). Resistance decides heating and the DC drop, the resistance page's territory; the two are independent facts about the same winding.
How does this pair with the magnetic-field page?
They are the same coil asked different questions: this page prices its inertia (how hard it fights change), that page prices its field (how hard it pushes on the world). Same turns, same length — the fields chain across the two pages.