A p-n junction does not obey Ohm's law. Its current rises roughly exponentially with applied forward voltage and saturates at a tiny value in reverse, and the standard description of that behaviour is the Shockley ideal diode equation. It is the first quantitative model of a semiconductor device most people meet, and it is accurate enough to be genuinely useful over several decades of current before its assumptions start to fail.
Arb Digital publishes free physics calculators that expose their parameters rather than hiding them. This page implements the Shockley relation in both directions, with saturation current, ideality factor, temperature and series resistance all under your control, and it is as explicit about where the model breaks down as it is about where it works.
What This Diode Current Calculator Does
In current mode you supply a voltage across the junction and get the current the ideal equation predicts. In voltage mode you supply a target current and get the forward voltage required to drive it. Both directions use the same relation, since the equation is analytically invertible.
The supporting numbers are the ones that actually explain the behaviour. The thermal voltage is the natural voltage scale of the junction and sets everything else. The exponent tells you immediately whether you are in the region where the −1 term still matters or deep in the exponential regime where it does not. The small-signal resistance is the slope of the curve at the operating point, which is what a signal riding on the bias actually sees. And the volts-per-decade figure is the practical rule of thumb: how much extra forward voltage buys a tenfold increase in current.
Series resistance is offered because without it the model diverges from reality badly at high current. With a non-zero value the tool solves the transcendental relation numerically rather than in closed form.
How to Use It
- Get the saturation current from the datasheet or a fit. It is not a universal constant. It varies over many orders of magnitude between a small-signal silicon diode, a Schottky and a power rectifier, and it depends strongly on temperature and on junction area.
- Set the ideality factor deliberately. One is the textbook ideal case dominated by diffusion current. Values approaching two indicate recombination in the depletion region, which is common at low currents and in wide-bandgap devices.
- Work in kelvin. The thermal voltage is proportional to absolute temperature, and 300 K is close to but not the same as room temperature at 293 K. Junction temperature under load is higher than ambient.
- Add series resistance once you are above a few tens of milliamps. Below that it barely matters; above it, it is what stops the model predicting absurd currents.
- Sanity-check the exponent. If it is very large the predicted current will be enormous and physically meaningless, and the page will say so rather than printing a number.
The Formula: The Shockley Diode Equation
The relation is
I = IS × ( eV/(nVT) − 1 )
where IS is the reverse saturation current, n is the ideality factor, and VT is the thermal voltage, defined as VT = kT/q with k the Boltzmann constant, T the absolute junction temperature in kelvin, and q the elementary charge. At 300 K the thermal voltage is 1.380649 × 10⁻²³ × 300 ÷ 1.602177 × 10⁻¹⁹ = 0.025852 V, or about 25.85 mV. Both constants are exact by definition in the present SI and are published by NIST's fundamental physical constants resource.
Work an example. Take IS = 1 × 10⁻¹² A, n = 1 and T = 300 K, and apply 0.6 V. The exponent is 0.6 ÷ 0.025852 = 23.209. Exponentiating gives 1.201 × 10¹⁰, so the current is 10⁻¹² × 1.201 × 10¹⁰ = 0.01201 A, about 12 mA. The −1 term is utterly negligible here, which is typical of any forward bias more than a couple of hundred millivolts.
Inverting for voltage gives V = nVT ln(I/IS + 1), and the −1 becomes a +1 inside the logarithm. Because a factor of ten in current costs nVT ln(10) in voltage, the practical rule is about 59.5 mV per decade at 300 K for n = 1, or roughly 119 mV per decade for n = 2. That single number explains why a diode's forward drop looks almost constant: getting from 1 mA to 100 mA, a hundredfold increase, costs only about 120 mV. The device physics behind the junction is set out on the Georgia State University HyperPhysics page on diodes.
The Ideality Factor and Thermal Voltage Conventions
Two conventions cause more confusion here than anything else, so it is worth being explicit about which ones this page uses.
The ideality factor n, sometimes written as the emission coefficient and often called simply the n-factor, appears in the exponent alongside the thermal voltage. This page uses the convention I = IS(exp(V/(nVT)) − 1), where VT = kT/q is the pure thermal voltage and n multiplies it. Some texts and simulator models instead fold n into a modified thermal voltage and write the exponent as V/VT′ with VT′ = nkT/q. The two are identical in effect but the symbols mean different things, and mixing them will double-count n. A value of 1 corresponds to a current dominated by diffusion across the junction; a value approaching 2 indicates that recombination in the space-charge region dominates, which is typical at low forward currents and in LEDs and other wide-bandgap devices. Real diodes are not described by a single n over their whole range: the effective value drifts with current, which is why a measured log-current-versus-voltage plot is not a perfectly straight line.
The thermal voltage is kT/q and nothing else. It is about 25.85 mV at 300 K and 25.26 mV at 293 K, a four per cent difference that propagates straight through the exponent. Rounding it to 25 mV, which is common in hand calculations, is fine for estimating a bias point and not fine for extracting parameters from measured data. Note also that the temperature that matters is the junction temperature, not the ambient: a diode carrying real current is hotter than the air around it, and the saturation current itself roughly doubles for every ten kelvin rise, which is why the forward drop of a silicon diode falls by around two millivolts per kelvin despite the thermal voltage rising.
Where the Model Breaks Down
The Shockley equation is a model with stated assumptions, and knowing where it stops describing a real device matters more than the arithmetic.
High injection. The derivation assumes low-level injection, meaning that the density of injected minority carriers stays well below the majority-carrier density in the quasi-neutral regions. Push the current high enough and that stops being true. The exponential slope changes character, the effective ideality drifts toward two, and eventually the junction voltage rises far more slowly with current than the ideal equation predicts.
Series resistance. At high current, the ohmic resistance of the bulk semiconductor, the contacts and the bond wires drops a voltage of its own. What the terminals see is the junction voltage plus I times that resistance, so the measured curve bends away from the exponential and toward a straight line. This is why the calculator offers a series resistance and solves the combined relation numerically when you use it.
Reverse breakdown. The equation predicts that reverse current saturates at −IS and stays there forever. Real diodes do not. Beyond a certain reverse voltage, avalanche multiplication or Zener tunnelling causes the reverse current to rise very steeply, and the ideal equation has nothing to say about it. Zener and avalanche diodes are operated deliberately in that region; ordinary rectifiers are destroyed there unless the current is limited. This page models no breakdown at all and will keep reporting a saturated reverse current regardless of how negative the voltage goes, which is a limitation of the model rather than a description of a device.
Recombination and leakage. Generation and recombination in the depletion region add a current the ideal derivation omits, dominating at low forward bias and inflating reverse leakage well above IS. Surface leakage adds more. This is why measured reverse current in a real part is often orders of magnitude larger than the saturation current fitted from the forward curve.
Datasheet values vary. There is no such thing as the saturation current of a silicon diode. It is set by the doping, the junction area, the material and the process, and it differs between manufacturers, between part numbers and, within a tolerance band, between individual devices from the same reel. Any number you take from a datasheet is a typical value at a stated temperature, and designing to the typical rather than the guaranteed limit is a familiar way to build something that works on the bench and fails in production.
Where This Sits Among the Other Circuit Tools
This page models one non-linear device. For the linear parts of the same circuit, the Ohm's law calculator, the voltage divider calculator and the current divider calculator cover the basics, while the resistor combination calculator and the resistor power rating calculator handle networks and dissipation. If your diode is an LED, the LED resistor calculator sizes the series resistor from the forward drop this page can estimate, and the resistor color code calculator reads the band you end up choosing. For the carrier physics underneath the junction, see the drift velocity calculator and the electrical mobility calculator.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Double-counting the ideality factor — this page puts n in the exponent alongside kT/q. If your source has already folded n into its thermal voltage, do not apply it twice.
- Using ambient temperature instead of junction temperature — a conducting diode runs hotter than the air around it, and the exponent is sensitive to the difference.
- Trusting the model at high current — above the low-injection regime, and once series resistance dominates, the ideal equation over-predicts current badly.
- Expecting it to describe reverse breakdown — the equation saturates at minus the saturation current no matter how negative the voltage. Real diodes avalanche, and the model does not know that.
- Treating a datasheet saturation current as exact — it is a typical value for one part at one temperature, and it varies by orders of magnitude across device types and by a wide margin within a single part number.
Related Free Tools From Arb Digital
Work the surrounding circuit with the Ohm's law calculator, the voltage divider calculator, the current divider calculator and the resistor combination calculator. Size components with the LED resistor calculator and the resistor power rating calculator, and identify them with the resistor color code calculator. For carrier transport in the semiconductor itself, see the drift velocity calculator and the electrical mobility calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Current equals the saturation current multiplied by the exponential of the applied voltage divided by the ideality factor times the thermal voltage, minus one. The thermal voltage is the Boltzmann constant times absolute temperature divided by the elementary charge, about 25.85 millivolts at 300 kelvin.
One for an ideal junction dominated by diffusion current, and up to about two where recombination in the depletion region dominates, which is common at low currents and in LEDs. The right answer comes from the datasheet or from fitting measured data, and a real device does not hold a single value across its whole current range.
The Boltzmann constant times the absolute junction temperature divided by the elementary charge. It is 25.85 millivolts at 300 kelvin and 25.26 millivolts at 293 kelvin. This page keeps it as the pure kT/q value and applies the ideality factor separately in the exponent.
Because the relationship is exponential. At an ideality factor of one and 300 kelvin, a tenfold increase in current costs only about 59.5 millivolts. Going from one milliamp to one hundred milliamps therefore adds around 120 millivolts, which is why a diode drop looks roughly constant in practice.
At high injection, where the assumption that injected carrier density stays below the majority-carrier density fails; at high current, where series resistance dominates the terminal voltage; and in reverse breakdown, where avalanche or Zener conduction takes over and the equation predicts nothing at all.
A current approaching minus the saturation current and staying there, because the exponential term collapses to zero once the reverse voltage exceeds a few thermal voltages. Real diodes leak considerably more than that through depletion-region generation and surface paths, and eventually break down entirely, neither of which this model describes.
Strongly. It rises roughly exponentially with temperature and approximately doubles for every ten kelvin, which outweighs the rise in thermal voltage. The net effect is that a silicon diode's forward drop at fixed current falls by around two millivolts per kelvin, a relationship used deliberately in temperature-sensing circuits.
Because the effective ideality factor drifts with current, series resistance bends the curve at the top, and recombination current dominates at the bottom. A real device is a composite of several conduction mechanisms, and the single-exponential model describes only the middle of the range well.
This tool is provided for educational use only. It implements an idealised device model that ignores high injection, recombination current, reverse breakdown and thermal runaway, and its output must not be used as a design margin for any circuit that handles mains voltage, significant power or a safety function. Component selection and thermal design for real hardware should be verified against the manufacturer's datasheet limits and by measurement.
