IDMT Relay Calculator

Parameters

Six inputs feed the relay model. This is what each one means, what it is measured in, the range it accepts, and where it changes the operating time.

Protection curve (five options)

The inverse time characteristic. Writing M for the plug setting multiple and TMS for the time multiplier setting, the calculator uses: standard inverse, operating time equals TMS multiplied by 0.14 divided by M raised to 0.02 minus 1; very inverse, TMS multiplied by 13.5 divided by M minus 1; extremely inverse, TMS multiplied by 80 divided by M squared minus 1; long time inverse, TMS multiplied by 120 divided by M minus 1; and definite time, which is simply TMS in seconds.

Gotcha. On the definite time setting the fault current no longer affects the answer at all beyond deciding whether the relay picks up. The time dial becomes the delay in seconds directly.

Time dial setting, TMS (dimensionless)

The multiplier that scales the whole curve. It is linear: doubling the time dial doubles the operating time at every current.

Typical range. 0.05 to 1.0, which is the range the compliance check enforces. Feeder relays commonly sit between 0.05 and 0.2, incomers between 0.2 and 0.5.

Gotcha. Below 0.1 the calculator raises a warning to confirm coordination, because very low settings leave little room for the downstream device to clear first.

Pickup current, Is (amperes)

The plug setting, that is the current at which the relay starts timing. Typically set at 1.1 to 1.3 times the maximum expected load current on a feeder, above the largest starting current on a motor circuit.

Gotcha. The compliance check compares this against the CT primary rating, so if you enter pickup as a secondary value and a large CT primary, the check will pass while the plug setting multiple is wrong.

Fault current (amperes)

The prospective current through the relay for the fault you are grading, at the location being studied. The field accepts 0.1 to 10000 A.

Gotcha, the important one. The plug setting multiple is simply fault current divided by pickup current, with no CT scaling applied. Both figures must therefore be expressed on the same side of the CT. Enter both as primary amperes, which is the clearer approach, or both as secondary amperes. Mixing a primary fault current with a secondary pickup current inflates the multiple by the CT ratio and returns an operating time that is far too fast.

CT ratio (text, primary and secondary)

The current transformer ratio, for example 400/5. It is used for two things only: reporting the secondary current the relay sees at the entered fault current, and checking that the pickup setting does not exceed the CT primary rating.

Gotcha. Only a slash is parsed. Entering 200:1 with a colon is read as a primary of 200 with the secondary silently defaulting to 5 A, so a 1 A secondary CT must be typed as 200/1. Text that cannot be parsed at all falls back to 100/5. The CT ratio never scales the plug setting multiple or the operating time.

System voltage (kilovolts)

The nominal primary system voltage, recorded so it appears on the exported report.

Gotcha. It does not enter any formula. Changing it does not change the operating time, the plug setting multiple, or any compliance check.

Assumptions and limits

What the tool assumes

• It implements the five IEC 60255 curve equations with a single set of published constants. It does not carry the IEEE and ANSI curve shapes, manufacturer-specific curves, or the reset characteristic that decides how a relay behaves on intermittent faults.
• The relay is treated as ideal. There is no minimum operating time floor, no timing tolerance, and no allowance for the current transformer ratio error, saturation, or transient response, all of which matter at high multiples of pickup.
• The plug setting multiple is a plain ratio of the two currents you enter. Nothing is scaled by the CT ratio.
• The result is the relay operating time only. Circuit breaker opening time, typically 40 to 80 milliseconds, must be added before you compare two devices.

What this calculator does not do

• It grades nothing on its own. It returns the operating time of one relay at one current. Coordination means running it twice or more and comparing the results yourself, then adding breaker time and a margin.
• No instantaneous or high-set element, no directional element, no earth fault element with its own settings, no thermal or negative sequence protection, and no cold load pickup or inrush restraint.
• No cable or transformer damage curve, so it cannot tell you whether the chosen setting protects the equipment as well as grading against the next device.
• The four compliance checks are generic sanity checks: pickup multiple above 1, operating time under 100 seconds, pickup at or below the CT primary rating, and time dial within 0.05 to 1.0. None of them is a grading check.
• If the plug setting multiple is 1 or less the relay never operates. The calculator returns an infinite operating time, which the results panel displays as Infinity, and issues a warning.

The engine is marked draft, and every result carries a note asking you to verify the curve against relay manufacturer test data. Use the output to sketch grading, then confirm settings against the current edition of IEC 60255 and AS 60255, against the relay manufacturer published curves and settings ranges, and against a full protection coordination study. Settings must be signed off by the person responsible for the installation before they are applied to a live relay. Nothing on this page has been validated or certified by a chartered professional engineer.

Worked examples

Three runs through the IEC 60255 equations exactly as the calculator implements them, with every current expressed in primary amperes so the plug setting multiple is right.

The five curves compared at one operating point

All five curves at a plug setting multiple of 20 and a time dial of 0.20, calculated with the same formulas as above.

The spread is more than thirty to one at this single operating point, which is why the curve choice matters at least as much as the time dial when you are grading against a downstream device.

IDMT Relay Curves for IEC 60255

Inverse Definite Minimum Time (IDMT) relays are the foundation of overcurrent protection coordination in industrial and utility electrical systems. Their defining characteristic is an operating time that decreases as the fault current increases: small overloads are tolerated for longer periods to avoid nuisance tripping, while large fault currents are cleared rapidly to prevent equipment damage. This calculator computes the operating time for all five standard IEC 60255 inverse curves at any given fault current and time multiplier setting (TMS), making it straightforward to verify relay coordination during protection design.

Key concepts

• IEC 60255 curve types. The five standard curves are Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI), Long Time Inverse (LTI), and Definite Time (DT). Each follows a different mathematical formula relating the current multiple to operating time. SI is the most common for general distribution protection. VI and EI curves trip faster at high fault currents, making them suitable for transformer inrush coordination and fuse grading.
• Time multiplier setting (TMS). The TMS, sometimes called the time dial, scales the operating time of the relay curve up or down. A lower TMS produces a faster trip time at the same current. TMS is the primary adjustment used to achieve selectivity (grading) between upstream and downstream relays.
• Pickup current (plug setting). The minimum current at which the relay starts to operate. It is usually set as a multiple of the current transformer (CT) secondary rating. The relay does not operate below this threshold. Setting the pickup correctly ensures the relay ignores normal load current and only responds to fault or overload conditions.
• Grading margin. To ensure selectivity, the operating time of the upstream relay must exceed the downstream relay by a grading margin of at least 0.3 to 0.4 seconds at the maximum through-fault current. This margin accounts for relay timing errors, CT errors, and circuit breaker operating time.

Common scenarios

1. Distribution feeder protection grading. An industrial site with a main incomer relay and three downstream feeder relays. All use Standard Inverse curves. The feeder relays are set with TMS 0.1 and the incomer with TMS 0.3, providing a 0.4 second grading margin at the maximum fault level. If a fault occurs on one feeder, that feeder relay trips first while the incomer acts as backup.
2. Transformer protection coordination. A 1000 kVA distribution transformer with an upstream utility relay on the HV side and LV circuit breakers on the secondary. The HV relay uses a Very Inverse curve to ride through the transformer inrush current (which decays quickly) while still providing fast clearance for sustained faults. The LV breakers are set to trip before the HV relay for any fault on the secondary side.
3. Motor feeder relay setting. A large motor draws 6 to 8 times full load current during starting for up to 10 seconds. The relay pickup is set above the full load current, and the TMS is set high enough that the relay does not trip during the starting transient. An Extremely Inverse curve may be chosen so that the relay is slow at moderate overcurrents (motor starting) but very fast at high fault currents (cable or busbar fault).