Dielectric Breakdown Estimator

Physics Electricity and Magnetism • Electric Potential and Capacitance

Written by STEM Calculators Team Published January 12, 2026 Updated February 24, 2026

9. Dielectric Breakdown Estimator

Estimate breakdown voltage using the linear relation $V_{bd}\approx d\,E_{bd}$ with a safety factor $SF$. For air, you can optionally enable a Paschen’s-law-style approximation vs. pressure and gap.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication. Example: 1e-3 means 1 mm.

Material + Inputs

Material library: Dielectric strength $E_{bd}$ (V/m): Gap $d$ (m): Safety factor $SF\ge 1$: Applied voltage $V_{\mathrm{applied}}$ (V): Air: Paschen approx: Pressure $p$ (Pa) [Paschen]: Paschen constant $A$ (1/(Pa·m)): Paschen constant $B$ (V/(Pa·m)): Secondary emission $\gamma_{se}$: Plot $V_{bd}(d)$: Plot span factor: Cursor fraction $f\in[0,1]$: Play speed:

Safety factor uses $V_{\max}=V_{bd}/SF$. If $V_{\mathrm{applied}}\ge V_{bd}$, breakdown is likely.

Ready

Steps

Enter values and click Solve.

Spark preview

Indicator (not to scale)

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Breakdown voltage vs gap (pan/zoom)

Drag to pan • wheel to zoom • double-click resets view

Hover: (d, V)=…

The cursor fraction $f$ places a dot along the plotted $d$-range (it does not change your input $d$).

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9. Dielectric Breakdown Estimator — Theory

1) Linear breakdown estimate

A simple engineering estimate assumes breakdown occurs when the electric field reaches the material’s dielectric strength: $E\approx E_{bd}$ . For a roughly uniform field across a gap $d$, the breakdown voltage is

\[ V_{bd}\approx d\,E_{bd}. \]

This is most reasonable for near-uniform fields (e.g., parallel plates) and clean, dry conditions. Sharp edges and points can cause much earlier breakdown.

2) Safety factor

A safety factor $SF\ge 1$ reduces the design maximum voltage:

\[ V_{\max}=\frac{V_{bd}}{SF}. \]

Safety factors account for variability in humidity, temperature, surface contamination, manufacturing tolerances, and aging.

3) Paschen’s law (gases, concept)

In gases, breakdown is strongly influenced by pressure $p$ and gap $d$ through the product $pd$. A commonly used form (conceptually) is:

\[ V_{bd}\approx \frac{Bpd}{\ln(Apd)-\ln\!\big(\ln(1+1/\gamma_{se})\big)}. \]

The constants $A,B,\gamma_{se}$ depend on the gas, electrode material, and conditions. This calculator uses a rough air-only approximation to show how $pd$ can matter.

4) Practical notes

Humidity & contamination can lower effective breakdown strength.
Sharp edges raise local field and can trigger corona or breakdown early.
Geometry matters: the linear model assumes near-uniform fields.
Vacuum breakdown is complex (field emission, microprotrusions) and is not captured by a simple $E_{bd}$ value.