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Capacitor — Reactance, Voltage Rating, Energy & Type Reference

A capacitor stores energy in an electric field between two conductive plates separated by a dielectric. This page covers the capacitive reactance formula X_C = 1 / (2πfC), the voltage rating selection rule, energy storage E = ½CV², series and parallel combinations, dielectric-type trade-offs (electrolytic, ceramic, film, tantalum, supercap), and power-factor-correction (PFC) bank sizing. Reviewed by a licensed PE.

Capacitor reactance and energy calculator

The site capacitor calculator computes capacitive reactance X_C, energy stored E, time constant τ = RC, and impedance combinations for series and parallel networks. Pair with the power-factor calculator for PFC bank sizing on industrial loads.

CALC.015 Capacitor · X_C · Energy · τ=RC · Network
Capacitive reactance

X_C = 1 / (2π · f · C). Capacitor passes high frequency, blocks DC. At resonance with an inductor (X_C = X_L), the LC tank passes one frequency.

Capacitive reactance X_C
— Ω
Pick a mode and enter values.
FORMULA · X_C = 1/(2π·f·C) SOURCE · IEEE STD 100 · IEC 60384

Capacitor formulas

Eq. 01 — Capacitive reactance SI
XC=12πfCX_C = \frac{1}{2 \pi f C}
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X_C = capacitive reactance (Ω)
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f = frequency (Hz)
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C = capacitance (F)
Eq. 02 — Charge stored SI
Q=C⋅VQ = C \cdot V
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Q = charge (coulombs)
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C = capacitance (farads)
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V = voltage across the plates (volts)
Eq. 03 — Energy stored SI
E=12CV2=Q22CE = \frac{1}{2} C V^2 = \frac{Q^2}{2 C}
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E = energy stored (joules)
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C = capacitance (F); V = voltage (V)
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Energy scales with V² — doubling voltage quadruples energy
Eq. 04 — Capacitors in parallel SI
Ctotal=C1+C2+⋯+CnC_{total} = C_1 + C_2 + \dots + C_n
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Capacitances add directly (same voltage across each)
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Total stored energy = sum of individual stored energies
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Parallel arrangement increases capacitance and ripple-current capability
Eq. 05 — Capacitors in series SI
1Ctotal=1C1+1C2+…\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots
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Series capacitors combine like parallel resistors
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Same charge through each; voltage splits inversely with capacitance
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Series arrangement increases voltage rating, decreases capacitance
Eq. 06 — Power-factor correction kVAR SI
Q=P⋅(tan⁡ϕ1−tan⁡ϕ2)Q = P \cdot (\tan \phi_1 - \tan \phi_2)
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P = real power (kW)
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φ₁ = current PF angle; φ₂ = target PF angle
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Q = capacitor bank size in kVAR

Standards governing capacitors

DocumentScope
IEC 60384 seriesFixed capacitors — performance and test methods (electrolytic, film, ceramic, tantalum)
IEEE Std 18Shunt power capacitors (PFC bank standard)
IEEE Std 1036Application of shunt power capacitors
UL 810Capacitors — safety standard for North America
UL 810AElectrochemical capacitors (supercaps)
IEC 60931Shunt power capacitors of the non-self-healing type for AC systems
NEC Article 460Capacitors — installation requirements (overcurrent, discharge resistor)

Reference: capacitor types and typical applications

TypeRangeVoltageToleranceBest for
Aluminum electrolytic1 µF – 1 F6.3–550 V±20 %DC bus filter, audio, switching power supply
Tantalum0.1–1000 µF2.5–50 V±10 %Mobile electronics, low-noise filtering
Ceramic class I (NP0/C0G)1 pF – 0.1 µF6.3 V – 5 kV±5 %RF / timing — stable
Ceramic class II (X7R/X5R)10 nF – 10 µF6.3 V – 100 V±10 % (drops with DC)Decoupling, bulk filter
Film (polypropylene)10 nF – 100 µF50 V – 2 kV±5 %Snubber, motor run/start, audio
Film (polyester / Mylar)1 nF – 22 µF50 V – 1 kV±10 %Low-cost coupling, general purpose
Orange drop (Sprague film)0.001–1 µF200 V – 600 V±5 %Vintage guitar tone, vacuum-tube amp
Mica1 pF – 0.1 µF100 V – 10 kV±1 %RF transmitter, precision oscillator
Supercapacitor (EDLC)0.1 F – 3000 F2.5–3 V cell±20 %Memory backup, regen brake, peak shaving
Power PFC oil-filled1 – 600 kVAR240 – 13 800 V±5 %Industrial power-factor correction
  1. Identify the application Energy storage (DC bus, flash, EV regen): pick high-capacitance electrolytic or supercap. Filtering / decoupling: ceramic, X7R 0.1–10 µF. Coupling / blocking: film 0.01–10 µF. Power-factor correction: oil-filled three-phase capacitor bank, kVAR-rated. Motor start / run: AC film capacitor 5–500 µF.
  2. Pick capacitance and voltage rating Capacitance from the load model (XC for AC, RC time constant for DC, energy budget for storage). Voltage rating ≥ 1.5–2× the worst-case DC bus or peak AC voltage to absorb transients (and to allow for end-of-life derate on electrolytics).
  3. Choose dielectric type Aluminum electrolytic — high capacitance, polarised, modest tolerance, limited life. Tantalum — smaller, more reliable, but failure mode is short-circuit. Film (polypropylene, polyester) — non-polarised, AC-rated, long life. Ceramic — small, non-polarised, but capacitance varies with applied DC voltage. Supercap — very high capacitance, low voltage (2.5–3 V cell).
  4. Verify ripple current and ESR For DC bus capacitors, the ripple current spec must exceed the actual ripple, otherwise the capacitor overheats. Equivalent series resistance (ESR) determines internal heating: P_loss = I²·ESR. Check the manufacturer datasheet at your operating frequency.
  5. For PFC banks, size in kVAR Q (kVAR) = P_kW × (tan φ_existing − tan φ_target). Example: 100 kW load at PF 0.85 → tan φ₁ = 0.620; target PF 0.95 → tan φ₂ = 0.329; Q = 100 × (0.620 − 0.329) = 29 kVAR. Use the power-factor calculator to size the bank.

Worked example — DC bus capacitor sizing for a 5 kW solar inverter

5 kW single-phase solar inverter with a 400 V DC bus. Compute the bus capacitor required to limit voltage ripple to 5 % at 120 Hz (twice the 60 Hz line frequency).

  1. DC bus power: P = 5 000 W = constant.
  2. Energy oscillation per cycle (single-phase): ΔE = P / (2π × 120) = 5000 / 754 = 6.63 J peak-to-peak.
  3. Peak-to-peak ripple voltage at 5 %: V_pp = 0.05 × 400 = 20 V.
  4. Required capacitance: C = ΔE / (V × V_pp) = 6.63 / (400 × 20) = 829 µF.
  5. Voltage rating: 450 V minimum (provides 12 % margin above 400 V); typical 500 V or 600 V for transient headroom.
  6. Result: 1000 µF / 500 V aluminum electrolytic (next stocked size). Verify ripple-current spec ≥ 6.5 A_RMS.

Comparison — capacitor vs. battery vs. inductor

AspectCapacitorBatteryInductor
Stores energy inElectric fieldChemical bondsMagnetic field
Energy density (Wh/kg)0.01–10 (supercap)30–250 (Li-ion)0.001–0.1
Power density (W/kg)1 000–100 000200–4 00010–1 000
Cycle life10⁶+500–5 00010⁶+
Charge / discharge speedmillisecondsminutes – hoursmilliseconds
Best forBurst power, filtering, ripple smoothingSustained energy deliveryCurrent limiting, energy transfer

Variants and related queries

Capacitor reactance (X_C) — frequency dependence

X_C = 1 / (2πfC) means a capacitor presents a frequency-dependent impedance. At DC the capacitor blocks current entirely (X_C = ∞); at infinite frequency it short-circuits. This is why capacitors are used as AC coupling (pass signal, block DC bias) and as bypass / decoupling (low impedance to AC noise on a DC supply rail).

Capacitor formula for current

I = C × dV/dt — the current through a capacitor equals its capacitance times the rate of voltage change. For a sinusoidal voltage V = V_m·sin(ωt): I = C·V_m·ω·cos(ωt) = (V_m / X_C)·cos(ωt). The current leads the voltage by 90° in a pure capacitor (the dual of an inductor where current lags by 90°).

Voltage rating of a capacitor and orange-drop

Voltage rating is the maximum DC (or peak AC) voltage that the capacitor can withstand long-term without dielectric breakdown. Common classes: 6.3 V, 10 V, 16 V, 25 V, 35 V, 50 V, 63 V, 100 V, 250 V, 400 V, 450 V, 630 V, 1 000 V. The famous Sprague "orange drop" is a polypropylene-foil film capacitor in 200, 400, or 600 V ratings, popular in vintage guitar and tube-amplifier tone-circuit work.

PFC capacitor calculator and capacitor reactance calculator

For industrial PFC, the kVAR needed = P_kW × (tan φ_old − tan φ_new). The site power-factor calculator handles the math; the capacitor calculator on this page handles X_C and energy-storage sizing for capacitor banks. Always include a discharge resistor per NEC §460.6 — bleeds residual charge after disconnect.

Energy stored in a capacitor (calculate)

E = ½CV². For a 1000 µF cap charged to 400 V: E = 0.5 × 0.001 × 160 000 = 80 J — enough to vaporise solder if discharged through a screwdriver. Safe-discharge protocols matter: NEC §460.6 mandates a discharge path that drops a power capacitor to less than 50 V within 1 minute (commercial) or 5 minutes (utility).

Frequently asked questions

What is a capacitor?
A capacitor is a passive two-terminal electrical component that stores energy in an electric field between two conductive plates separated by an insulating dielectric. When voltage is applied, charge accumulates on the plates with magnitude Q = C × V, where C is capacitance in farads. Capacitors block DC and pass AC, oppose voltage change (the dual of inductors which oppose current change), and store ½CV² of energy when fully charged.
What is the reactance formula for a capacitor?
Capacitive reactance: X_C = 1 / (2πfC), with X_C in ohms, f in hertz, and C in farads. At DC (f = 0), X_C = ∞ (capacitor is an open circuit). As frequency increases, X_C decreases — at 60 Hz a 10 µF capacitor has X_C = 265 Ω; at 1 kHz the same capacitor has X_C = 16 Ω. The current leads the voltage by 90° in a pure capacitor.
How to calculate the energy stored in a capacitor?
E = ½ × C × V², where E is energy in joules, C is capacitance in farads, V is the voltage across the plates. A 1000 µF (0.001 F) capacitor charged to 12 V stores E = 0.5 × 0.001 × 144 = 0.072 J = 72 mJ. The same capacitor at 24 V stores 0.288 J — quadruple, because energy scales with V². For DC link capacitors in EV inverters, this energy is what protects the IGBTs during commutation.
Do capacitors in parallel have the same voltage?
Yes — capacitors connected in parallel share the same voltage across their terminals (same as resistors in parallel). The total capacitance is the sum: C_total = C₁ + C₂ + … + C_n. The total stored charge is the sum of individual stored charges. Capacitors in series, by contrast, share the same charge but split the voltage inversely with capacitance: V_i = Q / C_i.
What is the voltage rating of a capacitor?
The voltage rating is the maximum DC voltage (or peak AC voltage) the capacitor can withstand long-term without dielectric breakdown. Common ratings: 6.3 V, 10 V, 16 V, 25 V, 35 V, 50 V, 63 V, 100 V, 250 V, 400 V, 450 V, 630 V, 1 000 V, 2 000 V. Always specify a capacitor with voltage rating ≥ 1.5–2× the actual circuit voltage to provide safety margin against transients and component aging. Exceeding the rating causes catastrophic failure (electrolytic blow-up, ceramic crack, film carbonisation).

Historic source — invention of the capacitor

The Leyden jar — independently invented by Pieter van Musschenbroek in Leiden and Ewald von Kleist in Pomerania around 1745 — was the first device capable of storing meaningful electrical charge. It established the basic capacitor architecture (two conductors separated by a dielectric) that every modern electrolytic, ceramic, film and supercap still follows.

Pieter van Musschenbroek & Ewald von Kleist — independent inventors of the Leyden jar → 1745–1746 — first storage of substantial electrical charge in a glass jar lined with metal foil; the prototype of every modern capacitor

Related calculators and references

Sources and further reading

  1. IEC 60384 series — Fixed capacitors for use in electronic equipment.
  2. IEEE Std 18 — Shunt Power Capacitors.
  3. IEEE Std 1036 — Application of Shunt Power Capacitors.
  4. UL 810 — Capacitors; UL 810A — Electrochemical capacitors.
  5. NEC §460 — Capacitor installation requirements.
  6. Sedra, A. S.; Smith, K. C. Microelectronic Circuits, 8th edition. Oxford, 2020.