Calculate Cockcroft-Walton voltage multiplier output from AC input voltage and number of stages, or find the input or stages needed for a target voltage.

Changing this convention reinterprets the voltage number. RMS conversion assumes a sine wave.

Diode-drop assumption
0.7 V is an approximation. Enter the device/operating-point value; zero gives ideal diodes.

Cockcroft-Walton Multiplier Formula

The calculator estimates a conventional half-wave Cockcroft-Walton ladder with equal capacitors. It supports peak or RMS sine input, a simplified fixed drop per diode, and a steady-load sag/ripple estimate. The following ideal formulas apply when load current and diode drop are zero. One stage is a doubler section with two capacitors and two diodes.

Vₒut = 2 × n × Vₚ
Vₚ = Vₒut / (2 × n)
n = Vₒut / (2 × Vₚ)
  • Vout = ideal no-load output voltage
  • Vp = peak input voltage
  • n = number of multiplier stages

Choose output voltage, required input voltage, or minimum whole stage count. The selected mode explicitly identifies required inputs. Loaded output is ideal output minus estimated diode drops and half-wave load sag. Stage mode searches whole counts from 1 through 1,000; more stages need not improve loaded output.

Select the input convention. RMS sine input is converted internally using:

Vₚ = sqrt(2) × Vᵣms

Voltage Unit Conversions and Result Meaning

Use these tables to check units and understand the model limits. The load model excludes ESR, leakage, parasitics, source impedance and startup; it is not a component-rating or safety assessment.

Unit Equivalent in volts Example
1 kV 1000 V 5 kV = 5000 V
1 V 1 V 250 V = 250 V
1 mV 0.001 V 500 mV = 0.5 V
Condition Effect on actual output
No load or very light load Closest to the ideal value from the calculator
Higher load current Output voltage drops below the ideal value
More stages Higher ideal voltage, but more ripple and voltage sag in real circuits
Low capacitor value or low frequency More ripple and poorer voltage regulation

Example Calculations

Example 1: Find output voltage

You have a 500 V peak input and a 4-stage Cockcroft-Walton multiplier. Select no load and zero diode drop to reproduce this ideal example. With the default 0.7 V per diode, the estimate is 3994.4 V before load sag.

Vₒut = 2 × 4 × 500
Vₒut = 4000 V

The ideal no-load output voltage is 4000 V, or 4 kV.

Example 2: Find number of stages

You want an ideal output of 12 kV from a 1.5 kV peak input. Select no load and zero diode drop for this ideal example.

n = 12000 / (2 × 1500)
n = 4

You need 4 stages for an ideal no-load output of 12 kV.

FAQ

Does the calculator use RMS or peak input voltage?

Select peak or RMS sine voltage. RMS conversion is automatic: 120 V RMS is about 169.7 V peak. Changing the input convention reinterprets the entered number.

Why is the real output lower than the calculated output?

The calculator separates ideal output, simplified diode drops, steady-load sag and ripple. A real circuit also has capacitor losses, source impedance, leakage, parasitics and startup behavior. The conventional half-wave equations use a small-ripple approximation.

Can the number of stages be a decimal?

A physical multiplier uses whole doubler stages. Enter a whole count from 1 to 1,000. In stage-solving mode the calculator returns the first whole count whose modeled loaded output reaches the target, or reports that no count in the supported range does so. This estimate does not establish safe circuit or component ratings.