Capacitance Calculator
Two 100 cm² plates 1 mm apart in air form a capacitance of 88.5419 pF, from C = ε₀εᵣA/d.
Vacuum/air 1, PTFE 2.1, polyethylene 2.25, paper 3.5, glass 5–10, water 80.
88.541878128 pF
Full answer, then cut to fewer decimals (not rounded):
- 88.541878128 pF
- 88.54187812 pF
- 88.5418781 pF
- 88.541878 pF
- 88.54187 pF
- 88.5418 pF
- 88.541 pF
- 88.54 pF
- 88.5 pF
- In nF
- 0.08854187813 nF
- In µF
- 0.00008854187813 µF
- In farads
- 8.854187813 × 10⁻¹¹ F
Step-by-step solution
- C = ε₀εᵣA ÷ d = (8.854187813 × 10⁻¹²) × 1 × 0.01 ÷ 0.001
- C = 8.854187813 × 10⁻¹¹ F = 88.54187813 pF
Capacitance Formula
C = ε₀εᵣA/d
coax C = 2πε L/ln(b/a); concentric spheres 4πε ab/(b − a); isolated sphere 4πε a
Worked Example
Two 100 cm² plates 1 mm apart in air:
- C = ε₀εᵣA ÷ d = (8.854187813 × 10⁻¹²) × 1 × 0.01 ÷ 0.001
- C = 8.854187813 × 10⁻¹¹ F = 88.54187813 pF
In µF: 0.00008854187813 µF · In farads: 8.854187813 × 10⁻¹¹ F
GATE tip
For a capacitor with two dielectric layers in series (d₁, ε₁ and d₂, ε₂), C = ε₀A/(d₁/εᵣ₁ + d₂/εᵣ₂). Side by side they are in parallel and their capacitances add.
More Electromagnetic Fields Calculators
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L = μ₀μᵣN²A / l
toroid: l = 2πR (mean radius); coax: L/length = (μ₀/2π) ln(b/a)
Example: A 200-turn air-cored solenoid, 20 mm in diameter and 100 mm long: Inductance L = 157.914 µH.
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Electric Field Calculator
E = q/(4πε r²), λ/(2πε r), σ/(2ε)
ε = ε₀εᵣ; potential of a point charge V = q/(4πε r)
Example: A 1 nC point charge, 1 m away, in air: Electric field |E| = 8.98755 V/m.
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Magnetic Field Calculator
B = μ₀I/(2πr) (wire), μ₀NI/(2R) (loop centre), μ₀μᵣNI/l (solenoid)
toroid B = μ₀μᵣNI/(2πR); H = B/(μ₀μᵣ)
Example: A long straight wire carrying 10 A, at 1 cm: Magnetic flux density B = 0.2 mT.
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Lorentz Force Calculator
F = q v B sin θ, F = B I L sin θ
orbit radius r = mv⊥/(|q|B); cyclotron frequency f = |q|B/(2πm)
Example: An electron moving at 10⁶ m/s at right angles to a 0.5 T field: Force F = 8.01088 × 10⁻¹⁴ N.
Frequently asked questions
What does the dielectric do?
It multiplies the capacitance by εᵣ: the same plates with mica (εᵣ ≈ 6) store six times the charge at the same voltage.
What is the capacitance of a coaxial cable?
C per metre = 2πε₀εᵣ/ln(b/a). Typical 50 Ω coax with polyethylene is about 100 pF/m.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Capacitance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/capacitance-calculator/
IEEE
Scientific Converters, "Capacitance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/capacitance-calculator/