Estimate breakdown voltage, spark gap distance, pressure, or gas temperature for dry air when any three values are known with a dry-air approximation.
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High Voltage Spark Gap Formula
The calculator estimates spark gap breakdown in dry air using a near-uniform electric field approximation. It uses a reference breakdown field of about 3,000,000 V/m at 1 atm and 20°C.
Rearranged formulas used when solving for a missing value:
- V = breakdown voltage, in volts
- d = spark gap distance, in meters
- P = gas pressure, in pascals
- T = gas temperature, in kelvin
- E0 = reference breakdown field for dry air, 3,000,000 V/m
- P0 = reference pressure, 101,325 Pa
- T0 = reference temperature, 293.15 K
If you leave voltage blank, the calculator estimates the breakdown voltage for the gap. If you leave distance blank, it estimates the required gap for the entered voltage. If you leave pressure or temperature blank, it rearranges the same relationship to solve for that gas condition. All inputs are converted to base units before the calculation, then converted back to the unit selected in the field.
Typical Dry Air Breakdown Values
At about 1 atm and 20°C, the approximation is close to 30 kV/cm, or 3 kV/mm, for a near-uniform field. Real spark gaps can vary because electrode shape, humidity, surface condition, and field nonuniformity affect breakdown.
| Spark gap distance | Estimated breakdown voltage | Condition |
|---|---|---|
| 1 mm | 3 kV | Dry air, 1 atm, 20°C |
| 5 mm | 15 kV | Dry air, 1 atm, 20°C |
| 1 cm | 30 kV | Dry air, 1 atm, 20°C |
| 2 cm | 60 kV | Dry air, 1 atm, 20°C |
Pressure and Temperature Reference Values
| Quantity | Value | Equivalent |
|---|---|---|
| Reference pressure | 101,325 Pa | 1 atm, about 14.696 psi |
| Reference temperature | 293.15 K | 20°C |
| Higher pressure | Increases breakdown voltage | Denser air is harder to ionize |
| Higher temperature | Decreases breakdown voltage | Less dense air breaks down more easily |
Example Calculations
Example 1: Find the breakdown voltage
Suppose the spark gap is 1 cm, the pressure is 1 atm, and the gas temperature is 20°C.
- d = 1 cm = 0.01 m
- P = 1 atm = 101,325 Pa
- T = 20°C = 293.15 K
The estimated breakdown voltage is 30,000 V, or 30 kV.
Example 2: Find the spark gap distance
Suppose the breakdown voltage is 15 kV, the pressure is 1 atm, and the gas temperature is 20°C.
- V = 15 kV = 15,000 V
- P = 101,325 Pa
- T = 293.15 K
The estimated spark gap distance is 0.005 m, or 0.5 cm.
FAQ
Is this the same as Paschen’s law?
No. This calculator uses a simplified dry-air field approximation, scaled by pressure and temperature. Paschen’s law models breakdown as a function of pressure-distance product and gas-specific constants. For small gaps, low pressure, non-air gases, or precision design work, Paschen’s law or test data may be more appropriate.
Why does pressure change the spark gap voltage?
Higher pressure means more gas molecules in the gap. Electrons collide more often, so a stronger electric field is needed to start and sustain an arc. In this approximation, breakdown voltage is directly proportional to pressure when distance and temperature stay constant.
Why can real spark gaps differ from the estimate?
The estimate assumes dry air and a near-uniform field. Sharp points, rough electrodes, humidity, dirt, altitude, airflow, and electrode material can change the actual breakdown voltage. Treat the result as an estimate, not a safety clearance or insulation design value.