# Tesla Coil Calculator - Tuning, Coupled Energy Transfer, Output Voltage

> Design a spark-gap Tesla coil: primary and secondary inductance, top-load capacitance, resonance and tap point, energy transfer, voltage and spark length.

- URL: https://qilingtools.com/en/physics/tesla-coil
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Enter the supply voltage, primary capacitor, flat-spiral primary, solenoid secondary and toroid top load. The tool uses Wheeler, Medhurst and other empirical formulas to get inductances, capacitances and resonant frequencies, and finds the primary tap that tunes the coil. The energy-transfer tab solves the two coupled RLC circuits with RK4, plotting the primary and secondary voltages and the energy beating between them, finds the first notch and can quench the gap there. There is also an animated spark display, notes on solid-state coils and a browser-synthesised singing-coil demo. A prominent safety warning sits at the top.

## How to use

1. Read the safety warning first, then on Coil design & tuning pick a preset or enter the supply, primary, secondary and top-load sizes
2. Check the secondary resonance and the tap needed; turn off auto-tune to move the tap by hand and see detuning
3. On Energy transfer, adjust the coupling k and primary resistance and watch the voltage envelopes and first notch
4. On Solid-state & musical coils, press a button to hear how pulse rate becomes pitch

## Features

- Wheeler inductance for the flat spiral primary and solenoid secondary, Medhurst self-capacitance, toroid or sphere top load
- Solves for the primary tap that tunes the coil and shows the detuning percentage
- Coupled RLC equations integrated with RK4: primary and secondary voltages, energy transfer and automatic first-notch detection
- Optional gap quench at a current zero, to compare quenched and unquenched behaviour
- Ideal and loss-included output voltage, energy per bang, average power and Freau’s spark-length rule
- Animated sparks, a DRSSTC explainer and a Web Audio musical-coil demo

## FAQ

### How does a Tesla coil reach hundreds of kilovolts?

Not through the turns ratio but by using resonance to move energy from a big capacitor to a small one. The primary capacitor stores ½CpVp², and magnetic coupling transfers most of it to a secondary capacitance of only tens of pF. Energy conservation gives Vs ≈ Vp√(Cp/Cs): with Cp = 20 nF and Cs = 28 pF that is a factor of about 27, turning 21 kV into over 500 kV, minus losses.

### Why must the primary and secondary be tuned to the same frequency?

Two resonant circuits only keep exchanging energy fully when their frequencies match. When detuned, only part of the energy transfers before it flows back, and the secondary voltage drops noticeably. The primary capacitor is usually fixed, so you tune by moving the tap clip along the primary spiral to change its inductance. The top load, nearby objects and the sparks themselves all change the secondary capacitance, so the real tap often ends up a fraction of a turn beyond the calculation.

### What is the first notch, and how do I choose the coupling k?

Once coupled, energy beats back and forth between primary and secondary; after about 1/(2k) cycles the primary energy reaches a minimum, the first notch. Ideally the spark gap quenches right then and the energy stays in the secondary. Spark-gap coils usually use k = 0.1–0.2: too low and transfer is slow so losses take a larger share; too high and the secondary voltage rises so fast it flashes over the winding.

### Can spark length be calculated accurately?

No. Spark length depends on the top-load shape, air pressure and humidity, pulse rate and whether the spark strikes a grounded target. Hobbyists use Freau’s rule of thumb: spark length in inches ≈ 1.7√P with P the input power in watts, so 500 W gives about 38 inches, nearly a metre. Treat the tool’s figure as an order-of-magnitude guide.

### How do musical Tesla coils make sound?

Each burst heats the air almost instantly and creates a small shock wave, a crack. A solid-state coil (DRSSTC) can control the number of bursts per second precisely: 262 per second sounds like middle C. Drive the burst rate from MIDI and the coil plays tunes. The demo synthesises the same pulse-train sound in the browser and only plays after you press a button.

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