Parallel-Plate Capacitor Calculator
From the plate area, the gap between the plates, and the dielectric constant, get the capacitance of a parallel-plate capacitor in picofarads and nanofarads.
Three inputs, one capacitance
Enter the plate area, the plate separation, and the relative permittivity and the calculator returns the capacitance C = ε₀ × εr × A / d in both pF and nF.
Mind the units
Area is in square metres (m²) and the gap is in millimetres (mm). The calculator converts the gap to metres for you — just don't enter the area in cm².
What is a parallel-plate capacitor calculator?
Plate area, gap, and dielectric in, capacitance out
A parallel-plate capacitor is two conductive plates facing each other with an insulating material — the dielectric — in between. A parallel-plate capacitor calculator turns three measurements into the one number that matters: the capacitance, or how much charge the device stores per volt applied. Bigger plates store more charge, a smaller gap packs the field tighter, and a dielectric with a high relative permittivity multiplies the effect. That makes these three inputs all you need for textbook problems, sensor design, sizing a homemade capacitor, or just understanding why a real capacitor has the value printed on it.
Enter the plate area, the separation, and the dielectric constant to get the capacitance in picofarads and nanofarads instantly.
One formula built from the area, the gap, the dielectric constant, and the constant ε₀ (the permittivity of free space, about 8.854 × 10⁻¹² F/m).
C = ε₀ × εr × A / dA is the overlapping plate area in square metres, d is the gap between the plates in metres (the calculator converts your millimetres for you), εr is the dimensionless relative permittivity of the dielectric, and ε₀ is the fixed permittivity of free space. Capacitance rises with area and with εr, and falls as the gap d grows — so to pack more capacitance into less space, you use big plates, a thin gap, and a high-permittivity dielectric.
Suppose you have plates of 0.01 m² (10 cm × 10 cm), a 1 mm air gap, and εr = 1.
Convert the gap
1 mm = 0.001 m — the formula needs the separation in metres.
Apply the formula
C = 8.854 × 10⁻¹² × 1 × 0.01 / 0.001 = 8.854 × 10⁻¹¹ F.
Scale the units
8.854 × 10⁻¹¹ F = 88.541878 pF = 0.088542 nF.
The capacitance tells you how much charge the capacitor holds for each volt across it — a higher number means more stored charge at the same voltage. The example value (about 88.54 pF for 0.01 m², a 1 mm air gap, and εr = 1) sits in the picofarad range, which is typical for small air-gap and trimmer capacitors. To grow that number you have three levers: enlarge the plates (capacitance is directly proportional to area), narrow the gap (it is inversely proportional to separation), or swap in a better dielectric. Slipping a sheet of mica (εr ≈ 6) or a ceramic (εr in the hundreds or thousands) into the same gap multiplies the capacitance by that factor — which is exactly how compact capacitors reach microfarads in a tiny package. The picofarad and nanofarad readouts are the same value in two scales: 1000 pF = 1 nF, so use whichever matches the part you are comparing against.
The formula is the ideal-capacitor model, so a couple of practical points are worth keeping in mind.
Ideal parallel plates and consistent units
This formula assumes two flat, parallel plates with a uniform field and ignores fringing — the field that bulges out at the edges, which matters most when the plates are small or far apart. It also assumes a single uniform dielectric filling the whole gap. Real capacitors add lead inductance and dielectric losses that this ideal model leaves out. Keep the area in square metres and the separation in millimetres as labelled; mixing cm² or metres for the gap will throw the answer off by powers of ten.