Capacitor Size Calculator
Choose a calculation mode, enter the known values, and get the required capacitance plus supporting outputs instantly. The Energy Storage mode solves C = 2E / V² and can reverse-solve for voltage or energy. Power Factor Correction mode finds the kVAR and capacitance bank needed to lift a lagging power factor to a target. Motor mode uses the standard rule-of-thumb for start and run capacitors. Reactance mode converts between capacitance and capacitive reactance at any frequency.
How to calculate the size of a capacitor
The required capacitor size depends on what the capacitor needs to do. For energy storage (photography flash, defibrillators, UPS hold-up), the governing equation is E = (1/2) C V², rearranged to C = 2E / V². For example, a camera flash that must deliver 5 J from a 330 V capacitor needs C = 2 × 5 / 330² = 92 μF. For power factor correction, the capacitance is determined by the reactive power deficit: C = Q_c / (2π f V²), where Q_c is the reactive power in VAR required to lift the power factor to the target value. Motor applications use rule-of-thumb ranges: starting capacitors are 75-100 μF per horsepower, and run capacitors are 15-25 μF per horsepower.
Energy storage mode: the E = ½CV² formula
A capacitor stores electrical energy in an electric field between its plates. The amount stored is E = 0.5 × C × V², where E is in joules, C is in farads, and V is in volts. This quadratic relationship means that a small increase in voltage produces a large gain in stored energy. Rearranged, C = 2E / V² gives the capacitance needed to store a required energy at a given voltage, and V = √(2E / C) gives the voltage that will charge a known capacitor to a required energy level. Practical applications include camera flash units (typically 100-1000 μF at 300-500 V), pulsed-power systems, rail-gun charging banks, and uninterruptible power supply hold-up circuits.
Power factor correction: why and how to size a capacitor bank
Inductive loads such as motors, transformers and fluorescent ballasts draw reactive (lagging) current that increases the apparent power a utility must supply without doing useful work. Power factor (PF = kW / kVA) measures the ratio of real to apparent power. A PF below 0.95 often incurs utility penalty charges. Capacitor banks supply leading reactive current that cancels the lagging reactive demand. The required reactive power is Q_c = P × (tan φ₁ − tan φ₂), where φ = arccos(PF). Converting to capacitance: C = Q_c / (2π f V²). For a 100 kW load at PF 0.75 on a 415 V / 50 Hz three-phase supply, correcting to PF 0.95 requires about 67 kVAR and 2,960 μF. Automatic power factor controllers switch capacitor stages in and out to follow load changes.
Motor capacitor sizing: start and run capacitors
Single-phase AC induction motors use capacitors to create the phase shift needed to generate a rotating magnetic field. Two types are used. Starting capacitors are large-value electrolytic types (typically 75-100 μF per HP, rated 165-220 V AC) connected only during startup via a centrifugal switch; they are disconnected once the rotor reaches 75-80% of rated speed. Run capacitors are smaller, oil-filled types (typically 15-25 μF per HP, rated 370-440 V AC) that remain in circuit continuously to improve efficiency and power factor. Both types must have an AC voltage rating at least 1.25 times the motor nameplate voltage. Using an undersized run capacitor reduces efficiency and may cause the motor to overheat; too large a value can also cause problems by advancing the phase angle too far.
Capacitive reactance and AC circuits
Capacitive reactance Xc = 1 / (2π f C) describes how strongly a capacitor opposes the flow of alternating current at a given frequency. Unlike resistance, reactance stores and returns energy rather than dissipating it, and the current through a capacitor leads the voltage by exactly 90 degrees. At DC (f = 0), Xc is infinite and no steady-state current flows. As frequency rises, Xc falls, making capacitors useful as high-frequency bypass elements: a 100 nF ceramic capacitor has Xc = 32 Ω at 50 kHz and only 3.2 Ω at 500 kHz. In RC low-pass filters, the -3 dB corner frequency is f_c = 1 / (2π R C). In LC circuits, resonance occurs at f_r = 1 / (2π √(LC)), at which point inductive and capacitive reactances cancel.
Capacitor unit conversions and typical application ranges
| Value (F) | Value (μF) | Value (nF) | Value (pF) | Typical application |
|---|---|---|---|---|
| 1 F | 1,000,000 | 1,000,000,000 | 1,000,000,000,000 | Supercapacitors, energy storage |
| 0.01 F | 10,000 | 10,000,000 | 10,000,000,000 | Large electrolytic, motor start |
| 0.001 F | 1,000 | 1,000,000 | 1,000,000,000 | Motor run / PFC banks |
| 100 μF | 100 | 100,000 | 100,000,000 | Power supply bulk filtering |
| 10 μF | 10 | 10,000 | 10,000,000 | Audio coupling, decoupling |
| 1 μF | 1 | 1,000 | 1,000,000 | Timing circuits, bypass |
| 100 nF | 0.1 | 100 | 100,000 | High-frequency bypass (ceramic) |
| 10 nF | 0.01 | 10 | 10,000 | RF decoupling, filters |
| 100 pF | 0.0001 | 0.1 | 100 | RF tuning, parasitic compensation |
| 1 pF | 0.000001 | 0.001 | 1 | RF/microwave trim capacitors |
Common capacitance values across electronics and power engineering.
Frequently asked questions
What is the formula for capacitor size?
The formula depends on the application. For energy storage: C = 2E / V² (farads), where E is the energy in joules and V is the voltage. For power factor correction: C = Q_c / (2π f V²), where Q_c is the reactive power in VAR, f is frequency in Hz, and V is voltage. For motor sizing, rule-of-thumb ranges apply: 75-100 μF per HP for starting, and 15-25 μF per HP for running.
What happens if I use a capacitor that is too small?
In energy-storage circuits, an undersized capacitor delivers less energy per pulse, which may not be enough to trigger a flash, start a motor, or hold up a power supply long enough. In motor circuits, an undersized run capacitor increases running current, reduces efficiency, and can cause the motor to overheat and fail prematurely.
What happens if I use a capacitor that is too large?
In motor circuits, too large a run capacitor over-compensates the phase angle, increases current draw and heat, and can also shorten motor life. In PFC banks, over-compensation produces a leading power factor, which many utilities penalise just as they do lagging PF. In bypass applications, excess capacitance can lower the corner frequency below the intended range, affecting circuit frequency response.
How do I convert between microfarads, nanofarads, and picofarads?
1 microfarad (μF) = 1,000 nanofarads (nF) = 1,000,000 picofarads (pF). To go the other way, 1 pF = 0.001 nF = 0.000001 μF. Power electronics uses microfarads; RF and audio circuits often use nF or pF. The reference table on this page lists common values and their equivalents across all four units.
What voltage rating should I choose?
Choose a capacitor whose voltage rating is at least 20-25% above the maximum voltage it will see in circuit. For motor capacitors, the standard recommendation is a rating of 1.25 times the motor voltage. For power supply capacitors, use at least 1.5 times the nominal DC bus voltage. Running a capacitor close to its voltage rating accelerates aging and increases failure risk.
Can I use this calculator for three-phase power factor correction?
Yes. Select "Power factor correction" mode, then choose "Three-phase" under System type. The calculator uses the correct formula for a three-phase capacitor bank: C = Q_c / (2π f V²), where V is the line-to-line voltage, and the capacitor current output accounts for the √3 factor in three-phase systems.
What is the difference between a starting capacitor and a run capacitor?
A starting capacitor is large (75-100 μF/HP), electrolytic, and rated for intermittent duty only. It is switched out of circuit by a centrifugal switch once the motor reaches 75-80% of rated speed. A run capacitor is smaller (15-25 μF/HP), oil-filled (non-polarised), rated for continuous AC duty, and remains in circuit permanently to improve running efficiency and power factor.