Shockley Diode Equation Calculator — Current, Voltage and Thermal Voltage

Background.

Every electronics course teaches that a silicon diode drops about 0.7 V, yet the equation that describes the junction contains no 0.7 anywhere. Shockley's ideal diode law, I = I_S(e^(V/nV_T) − 1), is a smooth exponential with no threshold at all. Take a junction with a saturation current of 1 pA at 25 °C: 0.6 V across it drives 13.8707 mA, and 0.7 V drives 679.9065 mA. The familiar forward voltage is just the region where the exponential reaches currents people notice, and a part with a smaller I_S reaches them higher up.

The law can be solved either way here, current from voltage or voltage from current, and each answer comes with the thermal voltage, the small-signal resistance and the bias counted in thermal voltages.

The junction is ideal. With no bulk series resistance, the equation predicts impossible currents above roughly 0.9 V, and those are refused rather than printed. There is no reverse breakdown, so nothing here describes a Zener, and temperature enters through the thermal voltage alone; the much stronger rise of I_S with heat is not modelled.

What is shockley diode equation calculator?

The Shockley equation gives the current through a p-n junction as a function of the voltage across it. I_S, the reverse saturation current, sets the scale of the whole curve and is the small leakage left under reverse bias. V_T = kT/q, the thermal voltage, is about 25.7 mV at room temperature. The ideality factor n, usually between 1 and 2, stretches the curve to fit a real device: in forward bias, each extra n·V_T of voltage multiplies the current by e.

How to use this calculator.

1. 01Choose whether to solve for current or for voltage, then enter the known side: volts across the diode (negative for reverse bias) or milliamps through it.
2. 02Enter I_S in picoamps and the ideality factor n. Both come from fitting measured or datasheet forward curves; n = 1 gives the textbook form.
3. 03Set the junction temperature in degrees Celsius. It changes the thermal voltage and nothing else.
4. 04Check the bias in thermal voltages: above about 5, the shortcut I ≈ I_S·e^(V/nV_T) is accurate to better than 0.7%.

The formula.

The thermal voltage comes from the Boltzmann constant k = 1.380649 × 10⁻²³ J/K and the elementary charge q = 1.602176634 × 10⁻¹⁹ C, both exact since the 2019 SI redefinition, with T in kelvin (°C + 273.15). At 25 °C that gives V_T = 25.6926 mV. One cited source offers the shortcut V_T = T/11,586, which gives 25.7336 mV at the same temperature, about 0.16% high; the constants are used instead.

Current follows I = I_S(e^(V/nV_T) − 1). The −1 is what makes the current exactly zero at zero volts and lets it settle at −I_S under reverse bias. In forward bias its share shrinks fast: at five thermal voltages it changes the result by about 0.7%, and at twenty it is negligible.

Solving for voltage uses V = n·V_T·ln(I/I_S + 1), the exact inverse, so a round trip returns the starting value. The small-signal resistance is the slope of the curve, r_d = n·V_T/(I + I_S), found by differentiating the current equation.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Engineering LibreTexts, 'Solar Basics' supplemental module, D. P-N Junction Diodes, §3 'Ideal Diode Equation'. Primary source for the form implemented, including the ideality factor: 'i(v) = I_S [exp(v/ηV_T) − 1]', with I_S the reverse saturation current, v the applied voltage where 'negative values indicate reverse bias', V_T the thermal voltage, and 'η is the emission coefficient, which is 1 for germanium devices and 2 for silicon devices'. The module also names the relation the 'Shockley ideal diode equation'. Its shortcut V_T = T/11,586 is NOT used here — see the note on the CODATA constants below, and the 0.16 % gap recorded on the page. Retrieved 2026-07-29.
2. [2]Don H. Johnson (Rice University), 'Electrical Engineering', Engineering LibreTexts §3.20 'The Diode'. Independent second authority for the same relation without an ideality factor: 'i(t) = I₀(e^(qv(t)/kT) − 1)', where q is 'the charge of a single electron', k is Boltzmann's constant, T is 'the diode's temperature in Kelvin' and I₀ is the leakage current. Also states 'kT/q = 25mV' at room temperature, against the 25.693 mV this page computes from the exact constants — agreement to the precision the source gives. Setting n = 1 makes this page's equation identical to Johnson's, which is why n = 1 is the default. Retrieved 2026-07-29.
3. [3]Bill Wilson (Rice University), 'Introduction to Physical Electronics', Engineering LibreTexts §1.9 'The Diode Equation'. Third treatment, used for the saturation-current guidance quoted in the field hint and the FAQ: the ideal equation I = I_sat(e^(qV_a/kT) − 1); the statement that q/kT ≈ 40 V⁻¹ at room temperature, i.e. kT/q ≈ 25 mV; that for real silicon diodes 'I_sat is such a small value (on the order of 10⁻¹⁰ amps)'; and a measured extraction giving 'I_sat = e^−19.68 = 2.89 × 10⁻⁹ amps'. Retrieved 2026-07-29.
4. [4]NIST Reference on Constants, Units and Uncertainty — CODATA 2022 recommended values. Boltzmann constant k = 1.380649×10⁻²³ J K⁻¹, listed as exact; elementary charge e = 1.602176634×10⁻¹⁹ C, listed as exact. Both are exact by definition following the 2019 revision of the SI, so the thermal voltage kT/q carries no uncertainty beyond that of the temperature itself. Source of every digit of the 25.6925791211 mV figure quoted on this page. Retrieved 2026-07-29.