Capacitive Transformerless Power Supply Calculator - Xc, current & zener sizing

A capacitive transformerless power supply is a low-power AC-to-DC converter that replaces the bulky mains transformer with a series 'dropping' capacitor whose capacitive reactance limits the current drawn from the line, and this calculator turns the mains voltage, line frequency, and dropping capacitance into the output current, the required capacitance for a target load, and the zener clamp voltage the regulator needs.

• • Small always-on loads: Size the dropper for low-current devices such as a relay, a Wi-Fi module, or an LED indicator that must stay powered from mains without the cost and size of a transformer.
• • Classroom AC-circuit problems: Show students how the same Xc = 1 / (2π f C) relation that sets capacitive reactance also fixes the current a capacitor passes when it is wired in series with the mains.
• • Zener clamp sizing: Find the clamp voltage V_z = V_out + V_d so the regulator diode and the rectifier are rated for the regulated rail you actually want.
• • Smoothing capacitor check: Estimate the reservoir capacitance needed to keep ripple within an allowed peak-to-peak band for a given load current.

The design is called 'transformerless' because the dropping capacitor does the current limiting instead of a magnetic transformer, which makes it cheap and compact but removes galvanic isolation - the low-voltage side is still tied to the mains through the capacitor and must never be touched or grounded.

The dropping capacitor's behavior is exactly the AC reactance this calculator finds, and the Capacitive Reactance Calculator shows how Xc = 1 / (2π f C) sets the current the supply can deliver.

The calculator treats the dropping capacitor as a fixed reactance in series with the mains, then applies the two standard AC relations to find the current it passes and the capacitance you would need for a chosen load.

• V_rms: RMS mains voltage across the dropping capacitor, typically 110, 120, 230, or 240 V.
• f: Line frequency in hertz, normally 50 Hz or 60 Hz.
• C: Dropping capacitance in farads; an X-rated safety capacitor must be used because it sits across the mains.
• V_out: Desired regulated DC output voltage after the zener clamp.
• V_d: Forward voltage drop of the clamping diode, about 0.7 V for silicon.
• I_load, ΔV: Target load current and allowed ripple used to size the smoothing reservoir capacitor.

Because Xc is usually far larger than the load impedance, the current is set almost entirely by the capacitor, so the output stays close to I_out = V_rms / Xc even as the load varies - up to the point where the load draws more than the capacitor can supply.

According to OpenStax University Physics Volume 2, the capacitive reactance of an ideal capacitor is Xc = 1 / (2π f C) and the current through it is I = V · 2π f C

According to HyperPhysics (Georgia State University), a capacitor blocks DC and passes AC, which is the principle a transformerless capacitive dropper uses to limit current without a transformer

Once the dropper current is known, the Ohm's Law & Basic Circuit Calculator relates that current to voltage and resistance so the load and clamp can be checked against the same numbers.

Four ideas explain why the result panel reads the way it does: reactance sets the current, the current is nearly load-independent, the zener sets the rail, and the capacitor must be X-rated.

The same 2π f that appears in Xc also appears in the ripple formula, so a higher line frequency both lowers the needed dropping capacitance and shrinks the smoothing capacitor for the same ripple.

Choosing the right X-rated part starts with the parallel-plate geometry, and the Capacitor Calculator turns dielectric and plate dimensions into the capacitance this supply depends on.

Enter the mains conditions and the capacitor you plan to use, then read the current, the required capacitance, and the zener voltage.

1. 1 Enter mains RMS voltage and frequency: Type the RMS mains voltage (for example 230 V) and the line frequency (50 or 60 Hz). These set the source the dropper sees.
2. 2 Enter the dropping capacitance: Type the series capacitor value in microfarads. Larger capacitance means more current; the calculator converts it to farads before the formula runs.
3. 3 Enter the output and regulator values: Type the desired output voltage, the clamp diode drop, the expected load current, and the allowed ripple voltage.
4. 4 Read Xc and I_out: Read the capacitive reactance and the output current the capacitor delivers from the mains.
5. 5 Read the required and smoothing capacitance: Read the capacitance you would need to hit the entered load current and the reservoir capacitance for the allowed ripple.

For a 230 V 50 Hz line with a 470 nF X2 capacitor and a 12 V output, the calculator returns Xc ≈ 6771 Ω, I_out ≈ 34.0 mA, V_z ≈ 12.7 V, and (for a 50 mA load and 1 V ripple) a required C ≈ 0.69 µF and smoothing C ≈ 500 µF.

The result panel reports capacitance in farads, and the Capacitance Conversion Calculator converts that value across the F, µF, nF, and pF ladder to match a real capacitor's marking.

The calculator collapses a reactance-plus-regulator sizing problem for a capacitive transformerless power supply into one result panel so you can compare capacitor values without re-deriving each formula.

• • No manual 2π f arithmetic: The form applies Xc = 1 / (2π f C) and I_out = V_rms / Xc for you, which removes the most error-prone step when comparing capacitor values.
• • Forward and reverse sizing: Both read the current from a chosen capacitor and the capacitance needed for a target load, so you can size in either direction.
• • Zener and smoothing in one view: V_z and the ripple-based smoothing capacitance appear alongside the current, which is the full set of numbers a small transformerless supply needs.
• • Mainline presets: The 50 Hz / 60 Hz and 110 to 240 V range covers the common residential mains so the numbers map straight onto a real schematic.
• • Traceable outputs: Every output traces to a single labelled formula, so the result can be checked against a textbook or a datasheet without guesswork.

Both a capacitive dropper and a resistive divider set a voltage from a source, and the Voltage Divider Calculator sizes the resistive version for comparison when isolation is not a concern.

Three inputs dominate the result of a capacitive transformerless power supply: the dropping capacitance, the mains voltage, and the line frequency; the load current and ripple set the smoothing capacitor.

• • The model assumes an ideal dropper capacitor and ignores the leakage and equivalent series resistance of real X-rated capacitors, so the real current is a little below the calculated value.
• • The calculator does not model the lack of galvanic isolation, component derating, inrush current, or rectifier losses; a transformerless supply is a shock hazard and must only be built by someone who understands mains safety and local electrical rules.

Transformerless supplies are best for a few tens of milliamps. Above roughly 100 mA the dropping capacitor becomes large and lossy, and an isolated switcher or a small transformer is the safer choice.

According to All About Circuits, a full-wave rectifier charges the reservoir capacitor twice per mains cycle, so the smoothing capacitor follows C = I / (2 f V_ripple), which this calculator uses to size the smoothing cap

Reactance and resistance both limit current, and the Electrical Resistance Calculator sizes the equivalent resistance if you compare a transformerless dropper against a resistive supply.