Compare nominal voltage and gap using an assumed uniform field of 3 MV/m. This educational arithmetic does not predict actual sparking, safe clearance or pressure/temperature effects.

Nominal-field arithmetic only, using 3 MV/m (3 kV/mm), a textbook atmospheric-air approximation. Does not predict actual breakdown or safe clearance. Pressure and temperature are not modeled.

Arithmetic scenarios around the assumed field; no confidence or safety meaning.

Related Calculators

High Voltage Spark Gap Formula

This calculator demonstrates nominal uniform-field arithmetic, V = Ed and d = V/E, using an assumed field of 3,000,000 V/m (3 kV/mm). This approximate atmospheric-air textbook value is not a universal spark threshold. Results do not predict actual breakdown, safe clearance or allowable working voltage.

V = E d
d = V / E
  • V = nominal voltage in volts.
  • d = gap distance in meters.
  • E = assumed uniform electric field, 3,000,000 V/m.

Choose Nominal voltage from gap or Nominal gap from voltage, enter the displayed value and select its unit. Changing a unit converts the entered quantity. Calculate returns the nominal answer and unit conversions. The initial 10% assumed-field sensitivity is an editable arithmetic scenario, with no confidence or safety meaning.

Nominal Field Examples

At an assumed 3 kV/mm, 1 mm corresponds to 3 kV, 5 mm to 15 kV, 10 mm to 30 kV and 20 mm to 60 kV. These are products of the chosen field and distance, not validated spark thresholds.

Example: voltage from distance

For d =1 cm =0.01 m, V =3,000,000 ×0.01 =30,000 V =30 kV.

Example: distance from voltage

For V =15 kV =15,000 V, d =15,000/3,000,000 =0.005 m =5 mm.

Assumed-Field Sensitivity

For a selected variation q, the lower and higher assumed fields are E(1−q) and E(1+q). At fixed gap, voltage varies directly with field; at fixed voltage, gap varies inversely with field. With ±10% field at 15 kV, the corresponding nominal gaps are 5.555556 mm at 2.7 MV/m and 4.545455 mm at 3.3 MV/m. This chosen span is not measured uncertainty or a safety factor.

Why Pressure and Temperature Prediction Was Removed

The previous version scaled breakdown voltage directly with pressure and inversely with absolute temperature, and could solve an equivalent pressure. That unrestricted model is not a validated prediction of gas breakdown. Actual breakdown depends on pressure-gap product, gas composition, temperature, electrodes and field geometry, and can have a Paschen minimum rather than changing monotonically with pressure.

NASA-HDBK-4007A describes an air minimum of approximately 327 V DC at a pressure-gap product of 0.7 Torr·cm. The former linear model gives about 27.6 V for a 1 mm gap at 7 Torr near room temperature. This counterexample shows why simply retaining the former pressure adjustment with a disclaimer would be misleading. This calculator therefore provides nominal V↔d arithmetic only.

FAQ

Is this Paschen’s law?

No. It uses a fixed assumed field. It does not model Paschen behavior or infer gas pressure or temperature.

Can it determine a safe air gap?

No. Electrical clearances and insulation coordination require the applicable equipment standards, voltage stresses and environmental conditions. A nominal field product is not design approval.

Why can real spark gaps differ?

Gas conditions, gap scale, sharp points, surface condition, electrode materials and nonuniform fields can change breakdown. The displayed nominal value should not be treated as a measured or allowable limit.

Sources: OpenStax, University Physics Volume 2, section 8.5 for the approximate air dielectric strength and V =Ed example; NASA-HDBK-4007A, pages45–47, for gas-breakdown and Paschen limitations.