Diode Equation Calculator
Shockley diode law I_D=I_S·(e^(V_D/(n·V_T))−1). Solve current or voltage, including reverse branch I_D > −I_S. Runs locally in your browser.
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 5/5 declared partitions (fwd-id, inv-vd, reverse-bias, small-x, invalid-domain) · Matrix
- Known limitations
- No series Rs / breakdown / recombination extras / high-injection. Is is specified at T, not computed from a reference-temperature value.
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Ideal Shockley diode I_D↔V_D, including reverse branch I_D > −I_S.
- Scope
- Ideal Shockley; no series Rs, breakdown, recombination extras, or high-injection
- Verification
- Engine tested · Source checked · v1.1.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.1.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-13.shockley-inverse-trust.2
- Verification revision
- 2026-09-13.shockley-inverse-trust.2 · 2/2 property · digest 4899855db55a
- Legacy regression
- 15/15 tests · Production surface contract 4/4
- Trust layers
- Verification VERIFIED · Production CURRENT · overall VERIFIED
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Internal · Pass · electrical-engineer
- Named expert review
- Not performed
- CVP suite
- 6/6 golden · 10/10 CVP boundary · 11/11 invalid · 2/2 property · 8/8 round-trip · 4/4 cross-interface · 4/4 CVP contract · Manifest
- Sources
- Shockley — The theory of p–n junctions in semiconductors and p–n junction transistors
- CODATA 2022 — Boltzmann constant k
- CODATA 2022 — elementary charge e
- Evidence
- 5 legacy golden · 6 legacy boundary · legacy regression suite · 6/6 oracle-backed golden · 11/11 invalid · Artifact integrity PASS · CalculatorX electrical review
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Choose I_D from V_D or V_D from I_D
Forward solve uses Shockley. Inverse uses V_D = n·V_T·ln(1+I_D/I_S) on the full domain I_D > −I_S, including I_D = 0 and reverse bias.
Enter I_S, ideality n, and temperature
I_S > 0 is the saturation current at this T. n > 0. Canonical temperature is T_K (default 300 K). REST/MCP also accept T_C, normalized to T_K.
Enter V_D or I_D
Read diode current or voltage. V_T = kT/q is computed from temperature. Large V_D/(n·V_T) returns NUMERIC_OVERFLOW rather than Infinity.
Example calculations
Common configurations with formula and result.
Si-like forward
V_D=0.7 · I_S=1e-12 · n=1 · 300 K
Diode Equation calculator specification
Version 1.1.0 · Engine tested · Supplemental domain review · Internal · 2026-09-13
- Engine tested 15/15 tests · Production surface contract 4/4
- Supplemental domain review Internal · Pass · electrical-engineer · 2026-09-13
- Named expert review Not performed
- Calculation version 1.1.0
Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)
- Definition
- The Shockley equation models an ideal p–n diode DC characteristic: I_D = I_S·(e^(V_D/(n·V_T))−1), with V_T=kT/q. Inverse: V_D = n·V_T·ln(1+I_D/I_S) for I_D > −I_S.
- What it calculates
- Ideal Shockley diode I_D↔V_D, including reverse branch I_D > −I_S.
- Inputs
- mode id|vd (default id)
- Vd (mode=id) or Id (mode=vd, Id > -Is)
- Is > 0 at selected T
- n (default 1)
- T_K (default 300; UI/query alias T_C normalized to T_K)
- Outputs
- Id or Vd
- Vt
- Formula
I_D=I_S(e^(V_D/(n·V_T))−1)- Assumptions
- Ideal Shockley; no series Rs, breakdown, recombination extras, or high-injection
- I_S is the saturation current at the selected junction temperature; I_S(T) is not derived
- Units
- V, A, K
- Boundary conditions
- Is,n,T ≤0 → VALUE_MUST_BE_POSITIVE
- mode=vd and Id ≤ -Is → VALUE_OUT_OF_RANGE
- binary64 overflow of expm1/log1p → NUMERIC_OVERFLOW
- Example
- Vd=0.7 Is=1e-12 n=1 T_K=300 → Id≈0.574755 A
- Validation cases
1 published on this page · 15/15 tests · Production surface contract 4/4 · View evidence
- id Vd=0.7 Is=1e-12 n=1 T_K=300 → Id≈0.574755
- Sources
- Shockley — The theory of p–n junctions in semiconductors and p–n junction transistors — Bell System Technical Journal 28(3), 1949 · 1949 · accessed 2026-09-13Supports: Ideal exponential Id–Vd relationship of a p–n junction
- CODATA 2022 — Boltzmann constant k — Fundamental Physical Constants · accessed 2026-09-14Supports: Vt = kT/q thermal voltage
- CODATA 2022 — elementary charge e — Fundamental Physical Constants · accessed 2026-09-14Supports: Vt = kT/q thermal voltage
- Shockley — The theory of p–n junctions in semiconductors and p–n junction transistors — Bell System Technical Journal 28(3), 1949 · 1949 · accessed 2026-09-13
- Last reviewed
- 2026-09-13
- Reviewed by
- CalculatorX electrical review (electrical-engineer)
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
Shockley diode I_D↔V_D. Ideal p–n model, including reverse bias down to I_D → −I_S⁺.
I_S is treated as the saturation current at the selected junction temperature. This calculator does not derive I_S(T) from a reference-temperature value. Changing T with I_S held fixed only updates V_T = kT/q.
Supported and not supported
Supported — Ideal Shockley forward and reverse DC · inverse I_D > −I_S (includes I_D = 0) · API electrical.diode.equation
Not supported — Breakdown, series R_s, capacitance, high-injection, SPICE models, automatic I_S(T)
Agent / API notes
Capability id: electrical.diode.equation · tool id: diode-equation · pin 1.1.0.
Defaults: mode=id, n=1, T_K=300. Canonical REST/MCP temperature is T_K. UI and query also accept T_C (Celsius), normalized to T_K; if both are sent, T_K wins.
mode=id requires Vd. mode=vd requires Id with Id > -Is. Id = 0 → Vd = 0.
Errors: MISSING_REQUIRED_INPUT, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, NUMERIC_OVERFLOW.
Related tools
Other calculators in this family: ADC Error Budget Calculator, LDO Thermal Calculator, LED Resistor Calculator, MOSFET Conduction Loss Calculator, MOSFET Junction Temperature Calculator, MOSFET Switching Loss Calculator, MOSFET Threshold & Overdrive Calculator, MOSFET Total Loss Calculator . Explore all Semiconductor.
Frequently asked questions
Key distinctions behind the calculation.
What is n?
Ideality factor, typically ~1–2 depending on recombination. n=1 is the ideal Shockley case.
What is saturation current I_S?
I_S is the scale of the exponential. In this calculator it is an input at the selected junction temperature T — not computed from a reference-temperature I_S(T) model. Changing T with I_S held fixed only moves V_T = kT/q.
What is thermal voltage V_T?
V_T = kT/q using CODATA 2022 exact k and e. At 300 K, V_T ≈ 25.852 mV.
Why is 0.7 V not a fixed diode drop?
Forward voltage depends on I_D, I_S, n, and T. 0.7 V is a silicon rule of thumb, not a constant. In this ideal model, 0.7 V at I_S=1 pA and 300 K already gives ~0.575 A — far above typical small-signal diode current because the model has no series resistance or high-injection limit.
How does temperature affect the result?
Only through V_T = kT/q. Real devices also have a strongly temperature-dependent I_S. This tool does not apply I_S(T); enter the saturation current that applies at the T you selected.
When does the Shockley equation stop being accurate?
When series resistance, self-heating, high injection, recombination-generation, or breakdown matter. Reverse current in the ideal model saturates at −I_S; real reverse leakage and breakdown are not modeled. Large V_D/(n·V_T) is numerically overflowed (NUMERIC_OVERFLOW) and is already outside the model.
Can I solve reverse bias?
Yes. Inverse mode allows I_D > −I_S, including I_D = 0 (→ V_D = 0) and I_D = −0.5·I_S. I_D ≤ −I_S returns VALUE_OUT_OF_RANGE.