This capacitance calculator works out a parallel-plate capacitor’s capacitance from plate area, separation and dielectric — and the charge and energy it stores at any voltage.
Scale reality-check: a farad is enormous — everyday capacitors live in pF–µF, with supercapacitors (double-layer, nanometer separations) the farad-scale exception. Combining capacitors: parallel adds (C₁ + C₂); series divides like parallel resistors (1/C = 1/C₁ + 1/C₂).
C = ε₀εᵣA ÷ d — Geometry Is Destiny
A capacitor’s value is set by three physical choices: more plate area (up), thinner gap (up), better dielectric (up). The stored quantities follow: Q = CV and U = ½CV² — note the square: doubling voltage quadruples stored energy, which is why voltage ratings are the safety-critical number on the can. Part of our Physics Calculators collection.
Worked Example (Verified)
- 100 cm² plates, 1 mm apart, glass dielectric (εᵣ = 5) (defaults): C = 8.854×10⁻¹² × 5 × 0.01 ÷ 0.001 = 442.7 pF · at 12 V: Q = 5.31 nC, U = 31.9 nJ
- Air-spaced same geometry: 88.5 pF — the dielectric alone bought a 5× improvement, which is the entire dielectric-materials industry in one ratio
- Why electrolytics win on size: their effective separation is an oxide layer nanometers thick — the d in the denominator does the heavy lifting no plate area can match
- Camera-flash scale: 300 µF at 330 V stores ½ × 300µ × 330² ≈ 16.3 J — real energy, delivered in a millisecond, hence flash capacitors’ respect-worthy discharge warnings
Practical Notes
- Real capacitors leak, age (electrolytics dry out), and carry tolerance codes (±20% is common, precision film ±1%).
- Breakdown voltage: every dielectric has a field strength limit; exceed it and the capacitor becomes a conductor, briefly and dramatically.
- AC behavior: capacitors pass AC with reactance Xc = 1/(2πfC) — the frequency dependence that filters, timers and our LC Resonance Calculator all stand on.
Related Tools
- LC Resonance Calculator — capacitors at work with inductors
- Electric Power Calculator — the wider circuit shelf
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate capacitance?
For parallel plates: C = ε₀ × εᵣ × A ÷ d, with ε₀ = 8.854×10⁻¹² F/m. Area in m², separation in m — 100 cm² at 1 mm with glass (εᵣ 5) gives 442.7 pF. Larger area, thinner gap, or higher-εᵣ dielectric all raise C.
How much charge and energy does a capacitor store?
Q = C × V and U = ½ × C × V². The energy’s voltage-square dependence is the key intuition: the same capacitor at 24 V stores four times the energy it does at 12 V, which is why voltage ratings matter more than capacitance for safety.
How do capacitors combine in series and parallel?
Parallel: capacitances add (more plate area, effectively). Series: reciprocals add (1/C = 1/C₁ + 1/C₂) — the opposite of resistors, because series stacking increases the effective plate separation. Two 100 µF in series give 50 µF; in parallel, 200 µF.
Why are most capacitors rated in µF or pF, not farads?
Because the farad is gigantic: a 1 F parallel-plate capacitor with a 1 mm air gap would need plates of ~113 km². Practical geometry yields picofarads to microfarads; supercapacitors cheat with nanometer gaps and porous electrodes to reach farads.
What does the dielectric do?
It polarizes, partially canceling the field between plates, which lets the plates hold more charge at the same voltage (× εᵣ). It also sets the breakdown voltage. Vacuum/air εᵣ = 1 is the reference; ceramics reach into the thousands at the cost of stability.
Is this capacitance calculator free?
Yes — free, instant, no sign-up.