Capacitors Formulas
Capacitor formulas describe how charge, energy, and voltage relate in capacitive components and how capacitors behave over time in RC circuits. These calculators handle stored energy, charge, and timing so you can design filters, timers, and energy-storage stages with confidence. They are central to power decoupling, signal coupling, and analog timing.
Capacitors Formula Calculators
- Capacitive Reactance Xc = 1 / (2πfC) Frequency 5 Hz, Capacitance 100 nF → Reactance = 0.3183 MΩ
- RC Time Constant τ = R × C Resistance 100 Ω, Capacitance 100 nF → Time Constant = 10 µs
- Capacitor Energy E = ½CV² Capacitance 100 nF, Voltage 0.33 V → Energy = 0.005445 µJ
- Capacitor Charge Q = C × V Capacitance 100 nF, Voltage 0.33 V → Charge = 33 nC
- Series Capacitance 1/Ctotal = 1/C1 + 1/C2 + ... + 1/Cn Capacitor Values 100 µF, 0.22 mF, 0.47 mF → 1/Ctotal = 6 × 10⁻⁵
- Parallel Capacitance Ctotal = C1 + C2 + ... + Cn Capacitor Values 100 µF, 0.22 mF, 0.47 mF → Ctotal = 0.79 mF
- Capacitor Impedance with ESR Z = √(ESR² + Xc²) ESR 0.1 mΩ, Capacitive Reactance 2.2 Ω → Total Impedance = 2.2 Ω
- Capacitor Ripple Voltage ΔV = I / (2 × f × C) Load Current 2 mA, Ripple Frequency 5 Hz, Capacitance 100 nF → Ripple Voltage = 2 kV
- Capacitor Self-Resonant Frequency f_SRF = 1 / (2π × √(ESL × C)) Equiv. Series Inductance 0.1 nH, Capacitance 100 pF → Self-Resonant Freq = 1.592 GHz
- Constant-Current Capacitor Charge Time t = C × ΔV / I Capacitance 100 nF, Voltage Change 0.33 V, Charging Current 100 µA → Charge Time = 0.33 ms
- Dielectric Dissipation Factor DF = ESR × 2πfC ESR 0.1 mΩ, Frequency 100 Hz, Capacitance 100 nF → Dissipation Factor = 6.28 × 10⁻⁹
- Ceramic Capacitor Voltage Derating C_eff = C_rated × factor Rated Capacitance 0.22 µF, Derating Factor 2.5 % → Effective Capacitance = 5.5 nF
- Capacitive Voltage Divider Vout = Vin · C1 / (C1 + C2) Input Voltage 0.726 V, Top Capacitor 100 pF, Bottom Capacitor 0.22 nF → Output Voltage = 0.2269 V
- Spherical Capacitor C = 4πε0 · a · b / (b − a) Inner Radius 0.1 mm, Outer Radius 0.22 mm → Capacitance = 0.0204 pF
Worked result for every Capacitors formula
| Formula | Expression | Worked result |
|---|---|---|
| Capacitive Reactance | Xc = 1 / (2πfC) | Frequency 5 Hz, Capacitance 100 nF → Reactance = 0.3183 MΩ |
| RC Time Constant | τ = R × C | Resistance 100 Ω, Capacitance 100 nF → Time Constant = 10 µs |
| Capacitor Energy | E = ½CV² | Capacitance 100 nF, Voltage 0.33 V → Energy = 0.005445 µJ |
| Capacitor Charge | Q = C × V | Capacitance 100 nF, Voltage 0.33 V → Charge = 33 nC |
| Series Capacitance | 1/Ctotal = 1/C1 + 1/C2 + ... + 1/Cn | Capacitor Values 100 µF, 0.22 mF, 0.47 mF → 1/Ctotal = 6 × 10⁻⁵ |
| Parallel Capacitance | Ctotal = C1 + C2 + ... + Cn | Capacitor Values 100 µF, 0.22 mF, 0.47 mF → Ctotal = 0.79 mF |
| Capacitor Impedance with ESR | Z = √(ESR² + Xc²) | ESR 0.1 mΩ, Capacitive Reactance 2.2 Ω → Total Impedance = 2.2 Ω |
| Capacitor Ripple Voltage | ΔV = I / (2 × f × C) | Load Current 2 mA, Ripple Frequency 5 Hz, Capacitance 100 nF → Ripple Voltage = 2 kV |
| Capacitor Self-Resonant Frequency | f_SRF = 1 / (2π × √(ESL × C)) | Equiv. Series Inductance 0.1 nH, Capacitance 100 pF → Self-Resonant Freq = 1.592 GHz |
| Constant-Current Capacitor Charge Time | t = C × ΔV / I | Capacitance 100 nF, Voltage Change 0.33 V, Charging Current 100 µA → Charge Time = 0.33 ms |
| Dielectric Dissipation Factor | DF = ESR × 2πfC | ESR 0.1 mΩ, Frequency 100 Hz, Capacitance 100 nF → Dissipation Factor = 6.28 × 10⁻⁹ |
| Ceramic Capacitor Voltage Derating | C_eff = C_rated × factor | Rated Capacitance 0.22 µF, Derating Factor 2.5 % → Effective Capacitance = 5.5 nF |
| Capacitive Voltage Divider | Vout = Vin · C1 / (C1 + C2) | Input Voltage 0.726 V, Top Capacitor 100 pF, Bottom Capacitor 0.22 nF → Output Voltage = 0.2269 V |
| Spherical Capacitor | C = 4πε0 · a · b / (b − a) | Inner Radius 0.1 mm, Outer Radius 0.22 mm → Capacitance = 0.0204 pF |
Variables used across Capacitors formulas
- Xc — Capacitive reactance in ohms (Ω)
- f — Frequency in hertz (Hz)
- C — Capacitance in farads (F)
- τ — Time constant in seconds (s)
- R — Resistance in ohms (Ω)
- E — Energy in joules (J)
- V — Voltage across the capacitor (V)
- Q — Charge in coulombs (C)
- Ctotal — Total equivalent capacitance (F)
- C1, C2, ... Cn — Individual capacitor values (F)
- Z — Total capacitor impedance (Ω)
- ESR — Equivalent series resistance (Ω)
- ΔV — Peak-to-peak ripple voltage (V)
- I — DC load current (A)
- f_SRF — Self-resonant frequency (Hz)
- ESL — Equivalent series inductance (H)
- t — Charge time (s)
- DF — Dissipation factor, also tan δ (dimensionless)
- C_eff — Effective capacitance at operating voltage (F)
- C_rated — Rated (zero-bias) capacitance (F)
- factor — Derating factor (0 to 1)
- Vout — Voltage across C2 (V)
- Vin — Total applied voltage (V)
- C1 — Top (series) capacitor (F)
- C2 — Bottom capacitor across the output (F)
- a — Inner sphere radius (m)
- b — Outer sphere radius (m)
- ε0 — Permittivity of free space (× εr if filled)
Questions people ask about Capacitors
- How to calculate esr from impedance for a capacitor — Capacitor Impedance with ESR
- Which 0402 capacitor value has a 1ghz self resonant frequency — Capacitor Self-Resonant Frequency
- Self resonant frequency for 0402 0.1uf capacitor — Capacitor Self-Resonant Frequency
- Ceramic capacitor derating factor — Ceramic Capacitor Voltage Derating
- Ceramic capacitor voltage derating calculator — Ceramic Capacitor Voltage Derating
- Capacitive voltage divider calculator — Capacitive Voltage Divider
- Capacitive divider formula — Capacitive Voltage Divider
- Spherical capacitor formula concentric spheres — Spherical Capacitor
Related Formula Categories
Browse the full formulas index for all 32 categories.