Wire Above a Ground Plane
A single conductor at height h above an infinite ground plane has a distributed capacitance determined by the geometry ratio 2h/r, where r is the wire radius. The electric field lines run from the wire to the ground plane.
h — Height from the centre of the wire to the ground plane surface.
Ground Plane — A large conductive surface (PCB copper, chassis, earth). Assumed infinite for the formula.
E-field — Electric field lines running from wire to ground. Their density determines the capacitance.
εr — Relative permittivity of the medium between wire and ground (1.0 for air, ~4.5 for FR-4 PCB).
Wire Capacitance Calculator
Every conductor near a ground plane forms a distributed capacitor. This parasitic capacitance affects signal integrity, loads high-impedance circuits, determines transmission line impedance, and contributes to crosstalk and EMI. Enter wire diameter, height above ground, and optionally length and dielectric permittivity — the calculator returns capacitance per metre, total capacitance, and characteristic impedance.
The Formula
Z0 = (60/√εr) × ln(2h/r) — characteristic impedance
h = height from wire centre to ground surface
r = wire radius (d/2)
ε0 = 8.854 × 10−12 F/m
εr = relative permittivity (1 for air)
The geometry ratio 2h/r is the single number that controls capacitance. Larger ratio (wire far from ground or thin) means lower capacitance and higher impedance. Smaller ratio (wire close to ground or thick) means higher capacitance and lower impedance.
Calculator Inputs
d (Wire Diameter) — conductor diameter in mm, inches, or AWG gauge (AWG 0–40 supported via built-in lookup). For insulated wire, use the conductor diameter, not the insulation outer diameter.
h (Height Above Ground) — distance from wire centre to ground surface, in mm, cm, or inches. For a PCB trace: the board thickness (typically 1.6 mm). For free-air wiring: the physical clearance to chassis or earth ground.
L (Wire Length) — optional. Multiplied by capacitance per metre to get total capacitance in picofarads.
εr (Relative Permittivity) — dielectric constant of the medium between wire and ground. Air = 1. FR-4 (PCB) ≈ 4.5. PTFE/Teflon ≈ 2.1. Polyethylene ≈ 2.3. Higher εr increases capacitance proportionally and decreases impedance.
Worked Example — Hook-Up Wire in Air
1 mm diameter wire, 10 mm above a ground plane, 100 mm long, air dielectric.
h = 10 mm = 0.01 m
2h/r = 2 × 0.01 / 0.0005 = 40
C/m = 2π × 8.854×10−12 × 1 / ln(40)
C/m = 55.63×10−12 / 3.689 = 15.1 pF/m
Total: 15.1 × 0.1 = 1.51 pF for 100 mm
Z0 = 60 × ln(40) = 60 × 3.689 = 221 Ω
1.5 pF from a 10 cm jumper wire. Negligible for most circuits, but in a high-impedance sensor front-end (10 MΩ+) or a fast comparator input, even a few pF of stray capacitance creates a low-pass filter that slows the signal. For the RC time constant this creates, see the RC Time Constant Calculator.
Worked Example — PCB Trace Over Ground Plane
0.5 mm wide trace, 1.6 mm above ground (standard 2-layer FR-4), 50 mm long, εr = 4.5.
h = 1.6 mm = 0.0016 m
2h/r = 2 × 0.0016 / 0.00025 = 12.8
C/m = 2π × 8.854×10−12 × 4.5 / ln(12.8)
C/m = 250.3×10−12 / 2.549 = 98.2 pF/m
Total: 98.2 × 0.05 = 4.91 pF for 50 mm
Z0 = (60/√4.5) × ln(12.8) = 28.28 × 2.549 = 72.1 Ω
~5 pF for a 50 mm trace. The FR-4 dielectric (εr = 4.5) increases capacitance by 4.5× compared to air at the same geometry. The 72 Ω impedance is close to 75 Ω — adjust trace width or board stackup to hit a specific target impedance for controlled-impedance routing.
Worked Example — Power Cable Above Earth Ground
AWG 12 conductor (d = 2.053 mm), 300 mm above earth ground, 10 m long, air.
h = 300 mm = 0.3 m
2h/r = 2 × 0.3 / 0.001027 = 584
C/m = 2π × 8.854×10−12 / ln(584)
C/m = 55.63×10−12 / 6.370 = 8.73 pF/m
Total: 8.73 × 10 = 87.3 pF for 10 m
Z0 = 60 × ln(584) = 60 × 6.370 = 382 Ω
87 pF over a 10 m run. At 50/60 Hz mains frequency this capacitance is negligible. But it matters for earth leakage current calculations in medical and safety equipment, and for EMI filter design where wire-to-ground capacitance provides a path for common-mode noise.
Dielectric Permittivity Reference
| Material | εr | Common Use |
|---|---|---|
| Vacuum | 1.0 | Theoretical reference |
| Air | 1.0006 | Free-air wiring (use 1) |
| PTFE (Teflon) | 2.1 | Coax insulation, RF boards |
| Polyethylene | 2.3 | Coax cable, wire insulation |
| FR-4 (fibreglass) | 4.2–4.7 | Standard PCBs (use 4.5) |
| Ceramic (alumina) | 9.8 | High-frequency substrates |
Higher εr increases capacitance linearly and decreases impedance by √εr. Moving from air (εr = 1) to FR-4 (εr = 4.5) increases capacitance 4.5× and cuts impedance by √4.5 ≈ 2.12×.
Why Wire Capacitance Matters
Signal Integrity
Parasitic capacitance on a signal trace forms a low-pass filter with the source impedance. A 10 pF trace capacitance with a 1 kΩ source gives τ = 10 ns — enough to round the edges of a 50 MHz clock signal. Faster signals need lower capacitance (shorter traces, thinner conductors, or lower-εr substrates).
High-Impedance Circuit Loading
A pH probe amplifier with 1012 Ω input impedance and 5 pF of wire capacitance has a time constant of 5 seconds. The wire capacitance dominates the circuit’s response time. Minimising wire length and using guard traces are essential in high-impedance instrumentation.
Transmission Line Impedance
The characteristic impedance Z0 of a wire over a ground plane comes directly from the capacitance geometry. A 50 Ω trace requires a specific width-to-height ratio at a given εr. The calculator shows Z0 alongside capacitance so you can verify both from the same inputs. For the underlying V = IR relationship, see the Ohm’s Law Calculator.
EMI and Earth Leakage
Wire-to-ground capacitance provides a path for high-frequency common-mode noise. In mains wiring, this capacitance couples noise from the live conductor to the safety earth. EMI filter design must account for it, and medical safety standards limit total earth leakage current — which is proportional to wire-to-ground capacitance × voltage × frequency.
Frequently Asked Questions
Last updated: March 2026