Capacitive reactance calculator

Use the calculator

Pick a mode at the top — Reactance, Energy, RC, or Network. Each mode has its own input set and emits a result with the calculation breakdown plus practical context (charge curve percentages, discharge time, equivalent circuit value).

The four capacitor formulas

The defining AC equation. Solve for C if you know X and f; for f if you know X and C. The formula is the exact dual of inductive reactance X_L = 2πfL — capacitors block DC and pass AC; inductors do the opposite. Combined in an LC circuit, they resonate at f₀ where X_C = X_L.

Energy scales with V², so doubling the voltage quadruples the energy. A 1 mF capacitor at 50 V holds 1.25 J — barely a spark. The same capacitor at 500 V holds 125 J — a destructive pulse. Always discharge bulk capacitors through a bleeder resistor before service.

The capacitor reaches 63.2 % of its final voltage after 1τ, 95.0 % after 3τ, and 99.3 % after 5τ — treated as "fully charged" for engineering purposes. Same curve applies to discharge. Used to set delays, smooth power-supply ripple, and form the cut-off of an RC low-pass filter at f_c = 1/(2π·R·C).

Series capacitors add reciprocally — exactly opposite of resistors. Two equal capacitors in series make half the value; in parallel make double. Series is used to handle high voltage with lower-voltage parts (each sees V/n); parallel is used to scale up bulk capacitance and to lower equivalent series resistance (ESR).

How to use the calculator, step by step

1. Identify what you need to find. Pick the calculator mode that matches your problem. Reactance: you have C and f and need X_C (or any one missing). Energy: you have C and V and want stored joules. RC: you have R and C and want the time constant. Network: you have multiple capacitors and want the equivalent.
2. Enter values in any consistent unit. The calculator accepts F / mF / µF / nF / pF for capacitance and Hz / kHz / MHz / GHz for frequency — pick whichever is natural and the conversion is internal. SI form uses farads and hertz.
3. Pick the right voltage rating for energy work. Stored energy scales with V². Doubling voltage quadruples energy. Always verify the capacitor's working-voltage rating exceeds the system voltage by 25–50 % margin — capacitors fail short-circuit when over-voltaged, often violently.
4. Use the RC charge / discharge curve. After 1τ a capacitor reaches 63 % of its target voltage; after 3τ, 95 %; after 5τ, 99.3 % (treated as fully charged). Same curve applies to discharge. Use τ to size timer circuits, debounce networks, and the cut-off frequency of low-pass filters.
5. Combine networks for non-standard values. Series capacitors add reciprocally — total is always smaller than the smallest. Parallel adds directly. Two 10 µF in parallel = 20 µF; two 10 µF in series = 5 µF. Series is also used to split voltage across lower-rated parts (each sees V/n, n parts in series).
6. Cross-check with the resonance condition for tuned circuits. When designing an LC tank, set X_C equal to X_L at the desired resonant frequency. The resulting LC product is fixed; pick L and C to match the impedance at f₀. Check by computing X_C with this calculator at the target f.

Reference values

X_C of a 10 µF capacitor at common frequencies

One reference capacitor across the AC frequency range — illustrates how quickly reactance drops with frequency.

Standard capacitor types and applications

Worked example: SMPS bulk capacitor sizing

A 100 W switching power supply has a 100 kHz switching frequency and needs to limit output ripple to 1 % of its 12 V output. Required capacitor value and reactance.

The reactance calculation gives 110 µF as the minimum, but real SMPS designs use 2–4× more (300–500 µF) to provide margin for component tolerance, capacitance loss with age, and to handle load-step transients. The ESR check is critical at 100 kHz — a high-ESR electrolytic adds resistive drop that ripple sees on top of pure X_C.

Variants and special cases

ESR — equivalent series resistance

Real capacitors have a small internal resistance from the leads, electrodes, and dielectric loss. ESR adds linearly to X_C, so impedance Z = √(ESR² + X_C²). At low frequency X_C dominates; at high frequency ESR becomes the limit and the capacitor stops behaving like a pure capacitor. Aluminium electrolytics have ESR 50–500 mΩ; polymer caps and ceramics push below 10 mΩ; vacuum and film capacitors below 1 mΩ.

Self-resonant frequency (SRF)

Every capacitor has a small parasitic inductance from its leads (ESL) that forms an LC tank with its own capacitance. Above the self-resonant frequency f_SRF = 1/(2π·√(L_ESL · C)), the capacitor looks inductive rather than capacitive. Decoupling caps on a PCB are picked so f_SRF lies above the highest noise frequency of interest — typical 0805 ceramic: 100 µF SRF ≈ 1 MHz, 1 µF ≈ 10 MHz, 1 nF ≈ 200 MHz.

Dielectric absorption ("memory")

After fully discharging a high-quality capacitor, some charge re-emerges over seconds to minutes from molecular relaxation in the dielectric. Polypropylene and Teflon are very low (< 0.05 %); aluminium electrolytics can be 10–15 %. Sample-and-hold circuits and integrators in precision instruments use polypropylene or polystyrene to minimise this error.

Variable-capacitance applications

Variable capacitors range from old air-spaced AM-radio tuners (10–500 pF) to modern silicon varactor diodes (1–100 pF, voltage-controlled) used in PLLs and frequency synthesisers. The frequency tuning range follows f₀ ∝ 1/√C — quadrupling C halves f₀.

The reactance equation in Steinmetz

The reactance of a capacitor in an alternating-current circuit is the absolute value of its impedance, and is inversely proportional to the frequency: X_C = 1 / (2π · f · C). At zero frequency, the reactance becomes infinite; at infinite frequency, it falls to zero — the capacitor approaches a short circuit at high frequency.

Related calculators and references

Frequently asked questions

What is capacitive reactance?

Capacitive reactance X_C is the AC opposition a capacitor presents to alternating current at frequency f. Unit: ohms. Formula: X_C = 1 / (2π · f · C). At DC (f = 0), X_C = ∞ — the capacitor blocks DC. At high frequency, X_C → 0 — the capacitor passes high frequency freely. This frequency-dependence is the basis of every capacitor application: filtering, coupling, decoupling, tuning.

What is the formula for capacitor reactance?

X_C = 1 / (2π · f · C), with X_C in ohms, f in hertz, C in farads. A 10 µF capacitor at 60 Hz has X_C = 1 / (2π · 60 · 10e-6) ≈ 265 Ω. Same capacitor at 1 kHz: X_C ≈ 16 Ω. Same at 100 kHz: X_C ≈ 0.16 Ω. Reactance drops by 10× when frequency increases 10×.

How much energy can a capacitor store?

E = ½ · C · V². A 1 000 µF capacitor at 400 V stores 80 J — enough to weld a screwdriver. A 1 F super-capacitor at 5 V stores 12.5 J. Defibrillators store 200–360 J at 1 500 V, delivered in a few milliseconds. Always discharge capacitors through a bleeder resistor before servicing equipment — the energy doesn't leak out on its own.

What is RC time constant?

τ = R · C in seconds. A 10 kΩ resistor with a 100 µF capacitor has τ = 1 second. The capacitor charges to 63 % of the supply voltage after 1τ, 95 % after 3τ, 99 % after 5τ. Discharge follows the same exponential curve. RC time constant determines: low-pass filter cut-off (f_c = 1/(2πRC)), timer-circuit period, button-debounce delay, and capacitor-discharge LED indicator brightness.

How do capacitors combine in series and parallel?

Series: 1/C_total = Σ(1/Cᵢ). Two 10 µF in series = 5 µF. Total is always smaller than the smallest single value. Used to split high voltages across lower-rated parts. Parallel: C_total = ΣCᵢ. Three 470 µF in parallel = 1410 µF. Total adds up. Used to build large bulk capacitance from cheaper standard parts and to lower ESR.

Why does the capacitor "block DC and pass AC"?

Reactance X_C = 1/(2πfC). At DC, f = 0, so X_C = infinity — current cannot flow. At high f, X_C is small — current flows easily. This is why coupling capacitors strip the DC bias from a signal, decoupling capacitors short high-frequency noise to ground, and filter capacitors smooth a rectified DC output (the AC ripple sees low X_C and is bypassed; the DC sees infinite X_C and passes through to the load).

Is X_C the same as impedance?

No — impedance Z is the total opposition combining resistance R and reactance X. For a pure capacitor, Z = X_C and the phase angle is −90° (current leads voltage). For a real capacitor at high frequency, Z = √(ESR² + X_C²), where ESR is equivalent series resistance. Z = R when there is no reactance (pure resistor); Z = X when there is no resistance (pure capacitor or inductor).

What is the difference between capacitive and inductive reactance?

Capacitive X_C = 1/(2πfC) — drops with frequency; phase: current leads voltage by 90°. Inductive X_L = 2πfL — rises with frequency; phase: current lags voltage by 90°. They are exact opposites and cancel at the LC resonance frequency f₀ = 1/(2π·√(LC)). Their cancellation is the operating principle of every radio tuner, RF filter, and switching power supply.

Sources and methodology

1. IEEE. IEEE Std 100 — The Authoritative Dictionary of IEEE Standards Terms, 7th Edition, 2000.
2. Steinmetz, C.P. Theory and Calculation of Alternating Current Phenomena. McGraw-Hill, 1897. Chapter VIII — capacitor reactance and impedance.
3. IEC. IEC 60384 — Fixed Capacitors for Use in Electronic Equipment, parts 1–22.
4. Maxwell, J.C. A Treatise on Electricity and Magnetism, 1873. Original derivation of stored energy E = ½CV².
5. BIPM. The International System of Units (SI), 9th Edition, 2019. Definition of farad, ε₀ = 8.8541878128 × 10⁻¹² F/m.
6. Pease, R.A. Troubleshooting Analog Circuits, Newnes / EDN Series, 1991. Practical capacitor selection and ESR / ESL discussion.