Shockley diode equation calculator

It evaluates I = Is × (exp(Vd / Vt) − 1), reports the current in amperes, and also returns the normalized voltage used by the exponential. The calculation is deterministic and runs without network access, making it useful for quick circuit checks, teaching examples, spreadsheet replacement, and repeatable engineering scripts.

Understand the Shockley diode equation

The Shockley equation describes the strongly nonlinear relationship between voltage across an ideal diode junction and the resulting current. In this calculator, Vd is the applied diode voltage in volts, Is is the reverse saturation current in amperes, and Vt is the thermal voltage in volts. The calculation is I = Is × (exp(Vd / Vt) − 1). A modest positive voltage can create a large forward current because voltage appears in an exponential, while a sufficiently negative voltage makes the exponential approach zero and the modeled current approach minus Is. That reverse-bias behavior represents saturation before breakdown; the equation does not model avalanche or Zener breakdown. Thermal voltage is approximately 25.85 millivolts near room temperature, but it is supplied directly so you can use a value appropriate to your assumptions. This form omits an ideality factor, so it corresponds to an ideality factor of one. Use a more detailed device or SPICE model when series resistance, recombination, high-level injection, self-heating, leakage variation, or breakdown materially affects the circuit.

Enter parameters with consistent units

Provide voltage and thermal_voltage in volts and saturation_current in amperes. Forward bias uses a positive voltage; reverse bias uses a negative voltage. All three inputs must be finite, while saturation current and thermal voltage must also be strictly greater than zero. For example, enter 0.6 V, 1e-12 A, and 0.02585 V to estimate forward current for a simplified silicon-junction case. Do not enter 25.85 for thermal voltage when you mean millivolts: convert it to 0.02585 V first. Likewise, a saturation current of one nanoampere is 1e-9 A, not 1. The response includes diode_current, the cleaned inputs, and normalized_voltage, which is Vd divided by Vt. That ratio is useful for checking why the result changes so sharply. The implementation uses expm1 rather than subtracting one from an ordinary exponential, which improves numerical accuracy around zero voltage. Inputs that would overflow the finite numeric range are rejected instead of returning Infinity, so automated callers receive a clear invalid-input failure rather than unusable JSON.

Use the result within the model's limits

Treat the returned current as the result of a compact analytic model, not as a guaranteed current for a particular manufactured diode. Saturation current can vary substantially between devices and with temperature, and thermal voltage itself depends on absolute temperature. Real circuits also include source resistance, diode bulk resistance, wiring resistance, and power limits that constrain the current predicted by an unconstrained exponential. The calculator is therefore most useful for coursework, sensitivity studies, first-pass hand calculations, regression fixtures, and comparing a known formula across many parameter sets. When designing hardware, verify the result against the component data sheet and include the surrounding circuit. In reverse bias, do not use this equation beyond the device's breakdown region because it intentionally has no breakdown term. Browser calculations run locally, while API automation costs $0.002 per successful request. Both channels use the same pure solver, so the same inputs produce the same JSON without a clock, random seed, external service, or hidden environmental dependency. Validation failures are reported before any result is produced.