The capacitor size calculator above answers one specific design question: how much smoothing capacitance does a DC supply need so that the voltage sags no more than a chosen amount between refills? It is the reservoir sizing problem that sits behind every linear power supply and every rectifier front end, and the arithmetic is short enough to do in your head once you have seen it.
Arb Digital builds free physics and electronics calculators that own one job properly. This page sizes a smoothing or filter capacitor for a DC rail. It does not size motor-run or motor-start capacitors, and the section below explains why that is a different and far more hazardous problem that belongs to a qualified electrician rather than to a web page.
What This Capacitor Size Calculator Does Not Cover
Motor-run and motor-start capacitors are mains-voltage components in a live appliance. They are specified by capacitance and by a voltage rating, a duty class and an application category, and those extra ratings matter every bit as much as the microfarads. A start capacitor is designed for a few seconds of duty per hour; a run capacitor is designed to sit energised continuously. Fitting the wrong class, or the right class with too low a voltage rating, causes overheating and destructive failure — venting, leakage, fire or a violent rupture — not merely poor performance. Getting the capacitance wrong also makes the motor draw the wrong current and run hot even when the capacitor itself survives.
For that reason this page publishes no capacitor selection table of any kind. The correct value for a motor is the one printed on the original part or specified by the equipment manufacturer, and replacing it is work for a qualified electrician who can isolate the supply, verify it is dead, discharge the capacitor safely and confirm the replacement matches on every rating. If you are here for an air-conditioner, a pump, a compressor or a single-phase motor, this is not the tool, and no online calculator is.
What follows is about low-voltage DC smoothing: the reservoir capacitor after a rectifier, or the bulk capacitor on a switching supply’s output. Even there, a rectifier fed from the mains puts the reservoir capacitor at rectified mains potential and it stores real energy that persists after the supply is switched off, which is what the energy figure in the results grid is for.
How This Differs From the Other Capacitor Tools
Three related pages on this site answer different questions and it is worth knowing which one you want. The capacitance calculator works forwards from physical construction — give it plate area, spacing and a dielectric and it tells you what capacitance those plates have. This page works backwards from a circuit requirement: given a current and a ripple budget, what capacitance does the circuit demand?
The capacitor charge time calculator takes a capacitor you already have and a resistor or a current source, and returns how long it takes to reach a target voltage. It is about the time axis for a known part. The capacitor energy calculator evaluates the energy and charge held by a part you have already chosen. In short: this page picks the value, and those pages analyse a value once picked.
How to Use It
- Choose the ripple source. A bridge rectifier refills twice per line cycle, so its ripple frequency is twice the line frequency. A half-wave rectifier refills once and needs roughly double the capacitance for the same ripple. A switching supply ripples at its switching frequency, which is usually tens or hundreds of kilohertz.
- Enter the worst-case load current, not the typical one. Ripple scales directly with current, so a supply sized for average load will sag badly at peak load.
- Set the ripple budget in peak-to-peak volts. A linear regulator downstream needs enough headroom that the ripple trough never falls below its dropout voltage, which is what usually sets this number.
- Enter the capacitance you can actually buy. Standard values are coarse and the grid will tell you the ripple that part really leaves, which is usually the more useful answer.
- Then check every other rating. Voltage, ripple current, equivalent series resistance, temperature and rated life all have to be satisfied by the same part. The capacitance is the easy half.
The Formula: How the Capacitance Is Calculated
Between refills the capacitor supplies the load on its own, and the defining relation of a capacitor is i = C dV/dt. Treating the load as a constant current over the gap gives C = I × Δt ÷ ΔV, and since the gap between refills is one ripple period, Δt = 1 ÷ fripple. That gives the standard result C = I ÷ (fripple × Vripple), with the ripple stated peak to peak. The definition of capacitance this rests on is set out in OpenStax University Physics Volume 2, section 8.1 on capacitors and capacitance, and the stored energy reported in the grid uses U = ½CV² from section 8.3 on energy stored in a capacitor.
The ripple frequency depends on the topology: full-wave rectification doubles the line frequency, half-wave leaves it alone, and a switching converter ripples at its own switching rate. Rectifier and filter design, together with the ripple-current and loss considerations this simple model leaves out, are treated in MIT OpenCourseWare 6.334, Power Electronics.
Work the defaults by hand. A full-wave rectifier on a 50 Hz supply ripples at 100 Hz, so the period between refills is 10 ms. Drawing 2 A and allowing 1 V peak to peak gives C = 2 ÷ (100 × 1) = 0.02 F, which is 20,000 µF. That is a large part, and it is why real designs either accept more ripple or put a regulator downstream. Fitting a 4,700 µF capacitor instead gives ripple of I ÷ (f C) = 2 ÷ (100 × 0.0047) = 4.26 V peak to peak, or 17.7 per cent of a 24 V rail. At 24 V a 20,000 µF capacitor holds ½ × 0.02 × 24² = 5.76 J.
Why This Formula Is Deliberately Pessimistic
The constant-current model assumes the capacitor discharges for the whole ripple period. It does not. The rectifier conducts for a short window near each peak and recharges the capacitor, so the actual discharge interval is shorter than a full period — typically 70 to 85 per cent of it in a mains rectifier with a substantial reservoir. The formula therefore asks for more capacitance than the circuit strictly needs, by roughly that margin.
That error runs in the safe direction and it is why the simple form is the one used in practice. Refining it means knowing the conduction angle, which depends on the transformer’s source impedance, the diode drops and the capacitance itself, so it is circular unless you simulate. Treating the answer as an upper bound and then choosing the nearest larger standard value is a reasonable engineering approach.
The model also assumes the ripple is a clean sawtooth produced by the discharge alone. In a real capacitor part of the ripple is produced by the charging current flowing through the equivalent series resistance, and that component is a sharp spike rather than a slope. In low-voltage, high-current supplies with fast switching, the resistive term can dominate entirely, which is why designers there parallel several capacitors to lower resistance rather than fitting one large one to raise capacitance.
Ripple Current Is the Rating That Actually Kills Capacitors
Every time the rectifier refills the capacitor it dumps a short, tall pulse of current into it. Averaged over a cycle that pulse has a root-mean-square value several times the DC load current, and it flows through the capacitor’s internal resistance, heating it from the inside. Electrolytic capacitors are rated for a maximum ripple current at a stated frequency and temperature precisely because that self-heating is what wears them out.
The wear mechanism is drying of the electrolyte, and its rate roughly doubles for every ten degrees of internal temperature rise. A part rated for two thousand hours at its maximum temperature can last far longer when run cooler, and far less than its rating when run hot in a sealed enclosure. This is why a capacitor chosen only on microfarads and volts can still fail within a year, and why data sheets quote a rated life alongside the electrical figures.
Two practical consequences follow. First, capacitance and ripple-current capability usually rise together within a family, so a part chosen with headroom on capacitance often has headroom on ripple current too — but you should confirm that rather than assume it. Second, dividing the job between several smaller capacitors in parallel shares the heat and lowers the combined series resistance, which is often better than a single large part. The capacitor combination calculator handles the arithmetic of parallel and series banks.
Voltage Rating, Headroom and Stored Energy
The voltage a reservoir capacitor sees is the peak of the rectified waveform, not the average DC rail, and the peak of a sine wave is about 1.414 times its root-mean-square value. On top of that, mains voltage varies, transformers regulate upward at light load, and an unloaded supply charges to the full peak with nothing drawing it down. A capacitor whose rating is only just above the nominal rail will be over-stressed in exactly those conditions, so real designs leave substantial margin. The rectified peak and diode drops are covered by the bridge rectifier calculator.
The energy figure in the results grid exists because of what that energy does. A charged reservoir capacitor holds its voltage after the supply is switched off and disconnected, and a bank of several joules at a few hundred volts is genuinely dangerous to touch and can weld a screwdriver tip. Bleeder resistors exist for this reason, and equipment that has them still needs the voltage verified as dead rather than assumed. If you are working on anything connected to the mains, treat the reservoir as live until you have measured it.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the line frequency for a full-wave rectifier — a bridge ripples at twice the line frequency, so using 50 or 60 Hz instead of 100 or 120 doubles the capacitance you think you need.
- Mixing peak-to-peak and RMS ripple — this formula is stated peak to peak. Feeding it an RMS figure asks for far more capacitance than the design requires.
- Sizing for average load current — ripple scales directly with current, so the worst-case load is the one that sets the value.
- Choosing on capacitance and voltage alone — ripple current, series resistance, temperature and rated life decide whether the part survives, and none of them appear in the capacitance formula.
- Treating this as a motor capacitor tool — motor-run and motor-start parts are mains-voltage components with duty classes and voltage ratings that this calculation does not address at all.
Related Free Tools From Arb Digital
Once you have a value, the capacitor energy calculator gives the energy and charge it will hold and the capacitor charge time calculator gives the time constants involved. The capacitance calculator works the other way, from physical construction to capacitance, and the capacitor combination calculator handles series and parallel banks. For the rectifier stage feeding it, use the bridge rectifier calculator; for how the capacitor behaves at a given frequency, the reactance calculator and the RLC impedance calculator; and for the load side, the Ohm’s law calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Divide the load current by the product of the ripple frequency and the allowable peak-to-peak ripple voltage. Two amps with one volt of ripple at 100 hertz needs 0.02 farads, or 20,000 microfarads. The result is a slight overestimate because the rectifier refills the capacitor before a full period has elapsed.
No. Those are mains-voltage parts specified by voltage rating and duty class as well as capacitance, and fitting the wrong one causes overheating and destructive failure rather than poor performance. Use the value on the original part or the manufacturer's specification, and have the work done by a qualified electrician.
Twice the line frequency for a full-wave or bridge rectifier, because it refills the capacitor on both halves of the cycle. The line frequency itself for a half-wave rectifier. The switching frequency for a switching converter, which is usually tens or hundreds of kilohertz and is why those supplies need far less capacitance.
Because it assumes the capacitor supplies the load for the entire ripple period. In reality the rectifier conducts near each peak and shortens the discharge interval, typically to 70 to 85 per cent of a period. The formula therefore errs on the generous side, which is the safe direction for a design estimate.
No. Larger reservoirs draw taller, narrower charging pulses, which increases peak diode and transformer current, worsens the power factor and raises the inrush at switch-on. They also cost more, take more space and store more energy that has to be discharged safely. Size for the ripple you need, with margin, not for the largest part that fits.
Because the charging pulses flow through the capacitor's internal resistance and heat it from the inside. That heating dries the electrolyte and is the main wear-out mechanism, with the rate roughly doubling for every ten degrees of temperature rise. A part correct on capacitance but run above its ripple-current rating will fail early.
More than the peak of the rectified waveform, which is about 1.414 times the RMS input, and with margin for high mains voltage and the light-load condition where nothing pulls the rail down. Rating a capacitor only just above the nominal DC rail leaves it over-stressed in exactly the cases that occur in normal use.
It can be. A reservoir capacitor holds its voltage after the supply is disconnected, and a few joules at a few hundred volts is enough to injure and enough to weld a tool tip. Bleeder resistors reduce the risk but do not remove the need to verify the voltage is actually zero before touching anything.
This tool is provided for educational and design-estimate use. It applies a simplified constant-current ripple model and does not account for conduction angle, equivalent series resistance, ripple-current heating, tolerance or rated life, so it does not select a component. Mains-connected equipment, motor capacitors and any installation work should be designed, carried out and verified by a qualified electrician or engineer against the applicable standard.
