IDMT Relay Trip Time Calculator

Inverse Time Overcurrent (TOC) protection, also called Inverse Definite Minimum Time (IDMT), describes a relay whose trip time automatically shortens as fault current rises, instead of tripping after one fixed delay no matter how severe the fault is. The relay compares the actual current it sees, I, against its own pickup setting, Is, and the ratio between them — I ÷ Is, commonly called PSM (Plug Setting Multiplier) or simply M — is the single number that drives how fast the relay operates on either the IEC or IEEE curve families below.

IEC 60255 formula: t = TMS × [k ÷ ((I÷Is)^α − 1)], where k and α are constants fixed by the specific curve (Standard, Very, Extremely, or Long-Time Standard Inverse — see the reference table below), and TMS (Time Multiplier Setting) scales the whole curve up or down without changing its shape.

IEEE C37.112-1996 formula: t = TD × [A ÷ ((I÷Is)^p − 1) + B], where A, B, and p are constants fixed by the specific curve (Moderately, Very, or Extremely Inverse), and TD (Time Dial) plays the same scaling role TMS plays in the IEC formula. The structural difference that matters here is the added constant B inside the brackets — it shifts every point on the curve by a fixed amount rather than only scaling the whole curve, which is why an IEEE curve's shape isn't simply a rescaled IEC curve even when their exponents look similar.

Worked example — IEC Standard Inverse: Is = 1000 A, I = 10,000 A, so PSM = 10. With k=0.140, α=0.020: (10)^0.020 ≈ 1.0471, so k÷(PSM^α−1) = 0.140÷0.0471 ≈ 2.971 s at TMS=1.0. At the default TMS=1.0 entered above, trip time ≈ 2.971 s.

Worked example — IEEE Moderately Inverse: using the same Is=1000 A, I=10,000 A (PSM=10), with A=0.0515, B=0.114, p=0.02: A÷(PSM^p−1) = 0.0515÷0.0471 ≈ 1.093, plus B=0.114 gives ≈ 1.207 s at TD=1.0 — noticeably faster than the IEC Standard Inverse curve at the identical PSM and multiplier value, illustrating why the two families aren't directly interchangeable setting-for-setting.

Why doubling fault current doesn't halve trip time: both formulas raise PSM to a fractional or low-integer exponent (α or p) before it enters the rest of the calculation, so the relationship between fault current and trip time is nonlinear — for the Standard Inverse curve's very small α=0.02 exponent in particular, trip time changes only modestly across a wide range of PSM values, with most of the curve's real speed variation concentrated at PSM values just above 1.

PSM must exceed 1 for the relay to operate: both formulas produce an undefined or negative result when PSM ≤ 1 (that is, when the actual current doesn't exceed the pickup setting) — physically this simply means the relay hasn't picked up at all yet and there is no trip time to calculate, not a calculation error.

Discrete relay taps versus continuous inputs: like the underlying pickup and TMS/TD settings themselves, this calculator treats Is, I, and the multiplier as continuous values, but many physical relays (especially older electromechanical types) only offer discrete tap steps for some or all of these settings — always round to the nearest available tap on the actual relay hardware, and re-run the calculation with the rounded value to confirm the achieved trip time still meets the original coordination requirement.

Matching the calculator's curve to the relay's actual configured curve: selecting the wrong curve type in this calculator — for example, calculating with an IEC Standard Inverse curve when the physical relay is actually configured for IEEE Very Inverse — produces a trip time that has nothing to do with what the real relay will do. Always confirm the exact curve type, and the exact standard family (IEC or IEEE), configured on the physical device before relying on a calculated trip time.

Where this calculator fits alongside a Relay Setting Calculator: a Relay Setting Calculator (solving backward from a desired trip time to the TMS/pickup that achieves it) and this trip-time calculator (solving forward from a known configuration to the resulting trip time) are complementary directions of the same underlying formula — use one to design a setting, and the other to sanity-check a setting you already have, whether it came from a prior coordination study, a relay's existing configuration, or this page's own comparison table below.

Summary: compute PSM = I ÷ Is, apply the correct curve family's formula (IEC's k/α form, or IEEE's A/B/p form) with the matching curve constants, scale by the actual configured TMS or TD, and always cross-check the result against the exact curve implemented on the physical relay and a complete multi-relay coordination study before finalizing any real installation.

1. Mixing IEC and IEEE constants in the same calculation. The IEC (k, α) and IEEE (A, B, p) constants belong to different formula structures — plugging IEC constants into the IEEE formula (or vice versa) produces a number that isn't a valid trip time for either standard.

2. Assuming a relay's country of origin tells you its curve family. Many modern numerical relays support both IEC and IEEE curve families in the same physical device, selectable per protection element — always confirm the actual configured family and curve type in the relay's own settings, not an assumption based on brand or region.

3. Confusing a manufacturer's Time Dial Multiplier (TDM) with the standard's Time Dial (TD). These are not always numerically the same value, and there is no single universal conversion between them — using a TDM value directly as TD in the IEEE formula, without checking the relay's own conversion, can produce a meaningfully wrong trip time.

4. Entering a fault current at or below the pickup setting. PSM must be greater than 1 for either formula to produce a valid, finite trip time — a fault current equal to or below pickup means the relay simply hasn't operated yet, not a calculation to solve.

5. Using CT secondary current where the relay's pickup is set in primary terms (or vice versa). Both I and Is need to be expressed on the same side of the CT ratio — mixing primary and secondary values anywhere in the PSM calculation produces a badly wrong ratio.

6. Assuming a calculated exact TMS/TD value is directly settable on the physical relay. Many relays, especially electromechanical types, only offer discrete tap steps for TMS/TD and sometimes for pickup current — always round to the actual nearest available tap and re-verify the resulting trip time, not just the theoretical calculated value.

7. Treating a single relay's trip time as proof of adequate coordination. A correctly calculated trip time for one relay says nothing about whether it's properly time-graded against the relays or fuses immediately upstream and downstream of it — coordination requires comparing operating times across every relevant device at every fault current of interest, not checking one relay in isolation.

8. Extrapolating a curve far beyond the fault current range it was designed for. Both curve families are defined and verified by their standards over a bounded PSM range typical of real protection applications — using extremely high or extremely low PSM values can produce numerically valid but practically meaningless results outside the range the relay manufacturer actually tested and published curve data for.