What is the capacitance formula?

The fundamental relationship is Q = CV, where Q is charge in coulombs, C is capacitance in farads, and V is voltage. Energy stored is E = ½CV². For a parallel-plate capacitor: C = εA/d (permittivity × area / plate separation).

How do capacitors combine in series and parallel?

Parallel: C_total = C₁ + C₂ + ... (capacitances add, like resistors in series). Series: 1/C_total = 1/C₁ + 1/C₂ + ... (reciprocals add, like resistors in parallel). Parallel increases capacitance; series decreases it. Series also increases voltage rating.

What units are used for capacitance?

Capacitance is measured in farads (F). Practical values are much smaller: microfarads (μF, 10⁻⁶ F) for power supplies, nanofarads (nF, 10⁻⁹) for filters, picofarads (pF, 10⁻¹²) for RF. Supercapacitors reach 1 F and up. A 1 F cap is enormous — pocket-sized supercaps are now available.

What happens if I reverse polarity on an electrolytic capacitor?

Disaster. Reverse voltage breaks down the dielectric (an aluminum oxide layer), causes gas formation, and can explode. Electrolytic and tantalum caps have a marked negative terminal (stripe) that must connect to lower voltage. Always check polarity before powering on.

Why does a capacitor block DC but pass AC?

At DC (0 Hz), the capacitor charges to source voltage and current stops — infinite impedance. At AC, voltage continuously changes, so charge keeps moving in and out, allowing current to flow. Impedance X_C = 1/(2πfC) decreases with frequency. Capacitors are AC short-circuits at high enough frequencies.

How long does a capacitor take to charge?

Through a resistor R, the time constant is τ = RC seconds. After 1τ: 63% of source voltage. After 5τ: ~99% (often called "fully charged"). For R = 10 kΩ, C = 100 μF: τ = 1 second, so ~5 seconds to full charge. Lower R or smaller C → faster charging.

What is ESR and why does it matter?

ESR is equivalent series resistance — the parasitic resistance inside a capacitor. Low ESR (~mΩ) is good for power supply filtering: less voltage ripple and heat. High ESR (electrolytic caps degrade over years) causes power supply instability and is why aging electronics often fail with bulging electrolytic caps.

How do I read capacitor markings?

Electrolytic: value and voltage printed directly ("100μF 16V"). Ceramic three-digit code: first two digits + zeros indicated by third. Example: "104" = 10 × 10⁴ pF = 100 nF = 0.1 μF. Tolerance letter: K = ±10%, M = ±20%, J = ±5%. Always check voltage rating on the body.

Capacitance Calculator

Calculate capacitance, charge, voltage, and energy stored in a capacitor. Uses Q = CV for charge-voltage relationship and E = ½CV² for energy. Also calculates series and parallel combinations.

Capacitance is the ability of a component to store electric charge. A capacitor consists of two conducting plates separated by an insulator (dielectric); when a voltage is applied across the plates, charge accumulates on them. The amount stored per volt is the capacitance, measured in farads (F). The relationship Q = CV is one of the foundational equations of circuit analysis.

This calculator computes the basic capacitor quantities: charge Q for a given capacitance C and voltage V, plus the energy stored E = ½CV². Capacitors are ubiquitous in electronics — every power supply uses them for filtering, every audio amplifier uses them for coupling, every digital chip uses them for decoupling. Their unique property: they pass AC but block DC, making them essential for signal coupling and noise filtering.

Capacitance values span twelve orders of magnitude in practice: from picofarads (pF, 10⁻¹²) in RF circuits, through microfarads (μF, 10⁻⁶) in power supplies, to farads (F) in supercapacitors used for energy storage. A 1 farad capacitor at 1 volt stores 1 coulomb — about 6.24 × 10¹⁸ electrons. Most everyday capacitors are far smaller; a typical electrolytic might be 100 μF, storing 100 microcoulombs per volt.

Common applications: power-supply smoothing, audio coupling/decoupling, timing circuits (RC time constants), tuned circuits (LC oscillators), camera flash energy storage, defibrillators, hybrid vehicle regenerative braking, and energy storage in renewable systems.

Inputs

Capacitance (μF)

Voltage (V)

Results

Charge

1200.00 μC

Energy Stored

7.2000 mJ

Capacitance

100 μF

Capacitance Results

Parameter	Value
Capacitance	100 μF (1.0000e-4 F)
Voltage	12 V
Charge (Q)	1.2000e-3 C (1200.0000 μC)
Energy Stored	7.2000e-3 J (7.200000 mJ)
Capacitance (nF)	100,000 nF
Capacitance (pF)	100,000,000 pF
Charge Formula	Q = CV
Energy Formula	E = ½CV²

Last updated: May 29, 2026

Formula

**Fundamental capacitor equations:** Q = C × V Where: - Q = charge (coulombs, C) - C = capacitance (farads, F) - V = voltage (volts, V) **Energy stored:** E = ½ × C × V² Alternative forms: E = ½QV = Q²/(2C) **Worked example: 100 μF capacitor charged to 12 V** C = 100 × 10⁻⁶ F = 0.0001 F V = 12 V Q = 0.0001 × 12 = 0.0012 C = 1.2 mC E = 0.5 × 0.0001 × 144 = 0.0072 J = 7.2 mJ **Common capacitance units:** | Unit | Value (F) | Used for | |---|---|---| | 1 F | 1 | supercapacitors | | 1 mF (millifarad) | 10⁻³ | rare | | 1 μF (microfarad) | 10⁻⁶ | power supplies | | 1 nF (nanofarad) | 10⁻⁹ | filters, timing | | 1 pF (picofarad) | 10⁻¹² | RF, antennas | | 1 fF (femtofarad) | 10⁻¹⁵ | chip-level | **Parallel-plate capacitor:** C = ε × A / d Where: - ε = permittivity of dielectric (ε₀ × εᵣ) - A = plate area (m²) - d = plate separation (m) - ε₀ = 8.854 × 10⁻¹² F/m Larger area → higher C. Smaller gap → higher C. Higher dielectric constant → higher C. **Common dielectric constants (εᵣ):** | Material | εᵣ | |---|---| | Vacuum | 1.000 | | Air | 1.0006 | | Paper | 3.5 | | Mica | 3-7 | | Ceramic (X7R) | ~3,000 | | Aluminum oxide (electrolytic) | ~8 | | Tantalum oxide | ~25 | | Water (RF) | 80 | | Strontium titanate | ~300 | **Series and parallel combinations:** **Parallel** (capacitances add, like resistors in series): C_total = C₁ + C₂ + C₃ + ... **Series** (reciprocals add, like resistors in parallel): 1/C_total = 1/C₁ + 1/C₂ + ... For two: C_total = (C₁ × C₂) / (C₁ + C₂) **Voltage divides in series:** V₁ = V_total × C₂/(C₁ + C₂) Smaller capacitor drops larger voltage — inverse of resistor behavior. **RC time constant:** τ = R × C (seconds) Charging: V(t) = V_max × (1 − e^(−t/τ)) Discharging: V(t) = V₀ × e^(−t/τ) After τ: 63% charged. After 5τ: ~99% charged. **Worked RC example:** R = 1 kΩ, C = 100 μF, V_source = 9 V. τ = 1000 × 100×10⁻⁶ = 0.1 s. After 0.1 s: V = 9 × 0.632 = 5.69 V. After 0.5 s (5τ): V ≈ 9 V (effectively full). **Capacitor impedance (AC):** X_C = 1 / (2πfC) Where f = frequency (Hz). Higher frequency → lower impedance. This is why capacitors block DC (X_C → ∞ at f=0) but pass AC. **Worked impedance example:** 100 μF at 60 Hz mains: X_C = 1/(2π × 60 × 100×10⁻⁶) = 1/0.0377 ≈ 26.5 Ω. **Capacitor types:** | Type | Range | Voltage | Notes | |---|---|---|---| | Ceramic | pF-μF | up to kV | small, cheap, common | | Electrolytic | μF-mF | up to 500 V | polarized, leakage | | Film (polyester, polypropylene) | nF-μF | up to kV | precision, stable | | Tantalum | μF | up to 50 V | small size, polarized | | Supercapacitor | F-thousands F | low (<5 V) | energy storage | | Mica | pF-nF | up to kV | high stability, RF |

How to use this calculator

Enter capacitance value with correct units (μF, nF, pF).
Enter voltage applied across the capacitor.
Calculator returns stored charge Q = CV and energy E = ½CV².
For series combinations, use 1/C_total = 1/C₁ + 1/C₂.
For parallel, C_total = C₁ + C₂.
For timing, use τ = RC and exponential charging/discharging curves.

Worked examples

Camera flash capacitor

**Scenario:** A camera flash uses a 500 μF capacitor charged to 300 V. Energy stored? **Calculation:** E = ½ × 500×10⁻⁶ × 300² = 0.5 × 5×10⁻⁴ × 90,000 = 22.5 J. **Result:** ~22 J of energy released in a millisecond — that's 22,000 W of instantaneous power, producing the bright flash. The capacitor lets a small battery (limited current) provide huge brief power output by storing energy gradually and dumping it suddenly.

Power supply smoothing

**Scenario:** A 12 V rectified DC supply has 100 mV of ripple at 120 Hz. The load draws 1 A. Required smoothing capacitor? **Calculation:** Approximate: C ≈ I / (f × V_ripple) = 1 / (120 × 0.1) ≈ 83 mF. Use a standard 10,000 μF (10 mF) capacitor for less ripple at the cost of size. **Result:** Need ~10,000 μF or more for clean DC with this load. Bigger capacitor = less ripple = cleaner power. This is why power-supply boards have those big cylindrical aluminum electrolytics.

RC timing circuit

**Scenario:** Design a 1-second delay with a 10 μF capacitor. What resistor? **Calculation:** τ = RC. For ~63% charge in 1 s: R = 1/C = 1/(10×10⁻⁶) = 100,000 Ω = 100 kΩ. **Result:** Use a 100 kΩ resistor. After 1 second, capacitor reaches 63% of source voltage. For ~99% (full-charge approximation), wait 5τ = 5 seconds. Used in 555 timer circuits, debounce filters, and analog signal processing.

When to use this calculator

**Use capacitor calculations for:**

- **Power supply filtering**: smoothing rectified DC. - **Audio coupling**: passing AC while blocking DC bias. - **Decoupling/bypass**: stabilizing IC power rails. - **Timing circuits**: RC oscillators, 555 timers. - **Tuned circuits**: LC resonance for radio, filters. - **Energy storage**: camera flashes, defibrillators, EV regen braking. - **Snubbers**: protecting switches from inductive transients. - **Motor starting**: phase-shift starting capacitors.

**Capacitor selection key parameters:**

- **Capacitance value**: μF, nF, pF range. - **Voltage rating**: must exceed maximum applied voltage; typically derate to 50-70%. - **Tolerance**: 5%, 10%, 20% common. - **Temperature stability**: X7R, NP0 vs Y5V (for ceramics). - **ESR (equivalent series resistance)**: matters for power supplies; lower is better. - **Ripple current**: max AC current rating without overheating. - **Polarized vs non-polarized**: electrolytics & tantalums are polarized.

**Common types and uses:**

- **Ceramic NP0/COG**: precision, RF, oscillators. - **Ceramic X7R**: general purpose decoupling. - **Aluminum electrolytic**: bulk power supply smoothing (polarized!). - **Film (polypropylene)**: audio, snubbers, precision filters. - **Tantalum**: compact decoupling (polarized, fail short). - **Supercapacitor**: energy storage, memory backup.

**Energy in supercapacitors:**

A 1 F supercapacitor at 2.7 V stores E = ½ × 1 × 7.29 ≈ 3.65 J. Compare: AA battery ~10,000 J. Capacitors lose to batteries on energy density but win on power density (release energy fast) and cycle life (millions of cycles vs hundreds).

**Common applications:**

- **Power electronics**: switching power supplies, inverters. - **Audio**: coupling capacitors, tone controls. - **RF**: tank circuits, antenna matching. - **Digital**: decoupling on every IC (typically 0.1 μF + 10 μF). - **Motors**: starting capacitors for single-phase motors. - **Automotive**: ignition, audio, regenerative braking caps.

**Safety:**

- Large/high-voltage caps store dangerous energy. Discharge before handling (TV tube caps, microwave oven caps, photo flash caps). - A 450 V × 1000 μF cap stores 101 J — enough to cause severe injury or death. - Use a bleeder resistor or discharge through a resistor (not a wire — explosive!) to safely dissipate.

**Pitfalls:**

- **Wrong polarity on electrolytics**: explodes or fails. - **Exceeding voltage rating**: dielectric breakdown. - **Ignoring temperature coefficient**: ceramic Y5V loses 80% C at extremes. - **Ignoring DC bias derating**: high-K ceramics lose capacitance under DC bias. - **Wrong units**: confusing μF with nF (factor of 1,000). - **Forgetting ESR**: high-ESR caps overheat and fail in power supplies.

**Reading capacitor markings:**

- **Three-digit code (ceramic)**: 104 = 10 × 10⁴ pF = 100,000 pF = 100 nF = 0.1 μF. - **Direct value**: "10μF 25V" printed. - **Tolerance letter**: K = ±10%, M = ±20%, J = ±5%.

Common mistakes to avoid

Connecting electrolytic capacitors with reversed polarity (causes failure or explosion).
Exceeding voltage rating (dielectric breakdown).
Mixing capacitance units (μF vs nF vs pF — factor of 1000).
Ignoring ESR in power supply applications.
Forgetting that high-K ceramics lose capacitance under DC bias and temperature.
Touching large charged capacitors without discharging first (electric shock risk).
Using wrong dielectric type for the application (Y5V where X7R is needed).
Forgetting series capacitance is smaller than smallest cap, not larger.

Frequently Asked Questions

Sources & further reading

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