Protection & Control calculator
IDMT Overcurrent Relay Curve Calculator
Operating time of an inverse-time overcurrent (ANSI 51) element for IEEE C37.112 and IEC 60255-151 curves, with a live time-current plot.
ProtectionBasis: IEEE C37.112-2018 · IEC 60255-151
Results
- Enter values to calculate
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Formula
IEEE C37.112: t = TD · [ A / (Mp − 1) + B ]
IEC 60255-151: t = TMS · k / (Mα − 1) with M = I / Ipickup
| Curve | A / k | B | p / α |
|---|---|---|---|
| IEEE moderately inverse | 0.0515 | 0.1140 | 0.02 |
| IEEE very inverse | 19.61 | 0.491 | 2 |
| IEEE extremely inverse | 28.2 | 0.1217 | 2 |
| IEC standard inverse | 0.14 | — | 0.02 |
| IEC very inverse | 13.5 | — | 1 |
| IEC extremely inverse | 80 | — | 2 |
| IEC long-time inverse | 120 | — | 1 |
Worked example
IEEE very inverse: pickup 600 A, fault 3000 A (M = 5), TD = 2: t = 2 × [19.61 / (5² − 1) + 0.491] = 2 × 1.308 = 2.62 s.
IEC standard inverse: M = 10, TMS = 0.1: t = 0.1 × 0.14 / (100.02 − 1) = 0.297 s.
Assumptions and standards
- Steady fault current; no DC offset or CT saturation. Check CT performance separately (IEEE C37.110).
- Time-dial ranges differ by relay manufacturer. Many North American relays apply the IEEE equation directly with TD from about 0.5 to 15; confirm against your relay’s instruction manual.
- Below M ≈ 1.1 most relays do not operate reliably; times there are shown for reference only.
- Add breaker interrupting time and a grading margin (typically 0.2–0.4 s) when coordinating with downstream devices.
Formula and data last verified: October 2026.
Frequently asked questions
Which curve do North American utilities use most?
IEEE very inverse and extremely inverse curves are common on distribution feeders, chosen to coordinate with reclosers and fuses. Moderately inverse is often used where fault current varies widely with source conditions.
What is the difference between TD and TMS?
Both scale the curve vertically. The IEEE equation multiplies by the time dial (TD), while the IEC equation multiplies by the time multiplier setting (TMS), typically 0.05–1.0.
Is this the same as an SEL U1–U5 or GE curve?
Manufacturer curves are close to, but not always identical to, the IEEE C37.112 constants. Use the manufacturer’s published equation for final settings.
Can I use these results for final design?
Use them for preliminary design and checking. Final designs must be verified by a qualified engineer against the code edition and standards adopted where the work is installed.
Is my data sent anywhere?
No. Every calculation runs in your browser. Nothing you type is uploaded or stored on our servers.