IDMT Relay Setting Calculator

An IDMT (Inverse Definite Minimum Time) overcurrent relay is the workhorse of power system protection — it monitors current through a current transformer (CT), and trips a breaker when current exceeds a set threshold for long enough, with an operating time that automatically decreases as fault current increases. Correctly setting one requires two separate decisions: where the pickup (plug) threshold sits, and how the time-current curve is scaled via the Time Multiplier Setting (TMS).

Step 1 — pickup (plug) setting: Pickup Current (primary) = Maximum Load Current × Margin (typically 1.25-1.3). This must sit above normal maximum load (so the relay doesn't trip on legitimate load) and below the minimum fault current the relay needs to detect. Plug Setting % = (Pickup Current ÷ CT Primary Rating) × 100, giving the percentage tap setting on the relay (most electromechanical and many numerical relays offer discrete plug setting taps, commonly in steps like 50%, 75%, 100%, 125%, 150%, 175%, 200% of rated current). The 1.25-1.3× figure is a simplified, preliminary starting margin for a quick calculation, not a universal protection-setting rule — real margin selection can depend on load characteristics, motor starting/inrush, transformer energization, permissible overload, relay and CT accuracy, and downstream coordination requirements, and should be confirmed against the specific application and the governing standard or utility practice.

Step 2 — Plug Setting Multiplier (PSM): PSM = Actual Fault Current ÷ Pickup Current Setting. This tells you how many multiples above pickup the relay actually experiences during a specific fault, and is the direct input to the time-current curve formula.

Step 3 — required TMS for a target operating time: using the IEC standard inverse (SI) curve, t = TMS × [0.14 ÷ (PSM^0.02 − 1)], rearranged to solve for TMS: TMS = Desired Operating Time ÷ [0.14 ÷ (PSM^0.02 − 1)].

Worked example: a 400/5 A CT protects a feeder with 300 A maximum normal load and 4000 A available fault current at the relay's location, with a desired 0.5 second operating time at that fault level. Theoretical Pickup Current = 300 × 1.25 = 375 A (Plug Setting = 375÷400 × 100 = 93.75%). PSM = 4000 ÷ 375 ≈ 10.67. Using the SI formula: 0.14 ÷ (10.67^0.02 − 1) ≈ 0.14 ÷ (1.0485 − 1) ≈ 0.14 ÷ 0.0485 ≈ 2.888 seconds at TMS=1.0, giving a theoretical TMS = 0.5 ÷ 2.888 ≈ 0.173. Since 93.75% isn't an available tap, select the next higher available tap (100%, giving an actual pickup of 400 A) and recalculate: PSM = 4000÷400 = 10.00, time at TMS=1.0 ≈ 2.971 s, so the recalculated TMS for the actual configured pickup is 0.5÷2.971 ≈ 0.168 — this recalculated figure, not the theoretical 0.173, is the one that reflects what the relay will actually do once a real tap is selected.

Why the relay curve flattens at high PSM: notice that PSM^0.02 changes very little even for large changes in PSM, since raising a number to the 0.02 power is a very gentle function — this is intentional in the standard inverse curve design, giving relatively modest additional speed improvement for very high fault currents beyond a certain point, since a relay already operating in well under a second doesn't need to get dramatically faster still for an even larger fault; the meaningful speed variation the curve provides is concentrated in the region just above pickup, where distinguishing marginal overload from genuine fault matters most for coordination purposes.

How TMS enables coordination between relays in series: consider two relays in series along a feeder, an upstream relay closer to the source and a downstream relay closer to the load, both seeing the same fault current for a fault beyond the downstream relay. If both relays used identical pickup and TMS settings, they'd operate at the same instant — a coordination failure, since the downstream relay should trip first, isolating only the affected downstream section. By giving the upstream relay a higher TMS (a scaled-up, slower curve) than the downstream relay, the upstream relay's operating time for the same fault current becomes deliberately longer, providing a time margin (a commonly cited illustrative range of 0.2-0.4 seconds, called the coordination time interval) for the downstream relay to operate and clear the fault first. Only if the downstream device fails to clear the fault does the upstream relay eventually operate as a backup, after its own longer delay has elapsed.

Relationship between plug setting taps and the calculated percentage: most relays, especially traditional electromechanical and many numerical models, offer plug setting only in discrete steps rather than continuous adjustment — common tap steps include 50%, 75%, 100%, 125%, 150%, 175%, and 200% of the relay's rated current. A calculated pickup requirement that falls between two taps (as in the worked example's 93.75%, between the 75% and 100% taps) needs an available tap that still satisfies the protection requirement. For this calculator's illustrative discrete tap-selection method, the next higher available tap is selected rather than whichever tap is numerically nearest, so the calculated load margin isn't reduced by rounding down — but this is a simplified selection method, not a universal protection-setting rule. Actual relay tap selection should also weigh minimum fault sensitivity, relay/CT characteristics, and coordination requirements, and must be verified against the specific relay model.

Numerical relay flexibility versus traditional tap-based settings: modern numerical (microprocessor-based) protection relays often allow much finer-grained, sometimes continuously adjustable, pickup and TMS settings compared to the discrete tap steps of older electromechanical relays, along with the ability to select from multiple curve types (and sometimes fully custom curves) within a single physical device. This flexibility doesn't change the underlying calculation principles covered here, but it does mean a numerical relay can often achieve a setting much closer to the theoretically calculated ideal value, rather than needing to round to a comparatively coarse traditional tap step.

Summary: use Pickup Current = Max Load × Margin (typically 1.25-1.3, a starting point rather than a fixed rule) for the plug setting, PSM = Fault Current ÷ Pickup Current, and TMS = Desired Operating Time ÷ [0.14÷(PSM^0.02−1)] for the Standard Inverse curve. Select the next higher available pickup tap so sensitivity margin isn't lost, then recalculate PSM and TMS at that actual pickup, and select an available TMS step according to your relay's own resolution and the coordination requirement (a lower nearby step trips faster, a higher one adds coordination margin) — then re-verify the operating time that step actually produces (see the recalculated figures in the result panel above). Verify the calculation against the actual curve type configured on the relay (Standard, Very, or Extremely Inverse each use different constants), and treat single-relay calculations like this one as one input into a broader, multi-device coordination study for a complete, safe protection design.

Where this calculation fits into a broader protection design workflow: a complete overcurrent protection study typically starts with a fault current analysis across the whole system (establishing maximum and minimum fault current at every relay location, for both close-in and remote faults), followed by pickup setting selection for every relay (ensuring adequate sensitivity margin above load, everywhere), then TMS coordination working from the most remote (downstream) relay backward toward the source, ensuring each successive upstream relay has adequate time margin over the one immediately downstream. This calculator addresses the pickup and TMS calculation for one relay at one operating point — the coordination sequencing across multiple relays is the additional, more involved step that a complete protection study performs.

This calculator gives you the tools to understand and independently sanity-check any single relay's setting within that larger process, whether you're reviewing an existing coordination study, learning the underlying principles, or performing a quick preliminary calculation before a full study is commissioned for a real installation.

Understanding why a relay is set the way it is — not just accepting a settings sheet at face value — is genuinely valuable for anyone responsible for a facility's protection system, since it enables meaningful review of settings inherited from a previous design, informed conversation with a protection engineer during a system upgrade, and faster diagnosis when an unexpected trip (or an unexpected failure to trip) occurs during a real fault event.

The calculator above solves one specific case — an IEC Standard Inverse overcurrent relay on a single HV/MV circuit. In a real distribution system, that relay is only one link in a chain of protective devices running from the incoming HV/MV transformer down to the individual LV loads it feeds, and each link in that chain is set with a different philosophy depending on where it sits. The two ends of that chain — the LV release at an end-use load, and the HV/MV relay further upstream — are worth understanding separately, since neither is a smaller or simpler version of the other.

LV release setting for end equipment (motors, capacitor banks)

An LV circuit breaker's release feeding a single, specific piece of equipment — a motor, a capacitor bank — sits at the very end of the distribution chain. There's no further downstream breaker or cable protection to coordinate with beyond that point, so its instantaneous (short-circuit) element may often be set to trip with minimal intentional delay, subject to the breaker manufacturer's own trip-unit limits, the equipment's actual starting/inrush characteristics, and any coordination requirements that still apply: any current that clearly exceeds the equipment's own starting/inrush behavior is generally treated as a genuine internal fault rather than a condition that benefits from a graded delay. This is different from a feeder breaker further up the chain that still has other breakers or cable runs downstream needing to clear first.

Two nameplate quantities drive this setting: FLA (Full Load Ampere — the motor's rated running current, used for the thermal/overload element) and LRA (Locked Rotor Ampere — the much higher current drawn momentarily while the motor accelerates from standstill, used to keep the instantaneous element from tripping on a normal start). The instantaneous pickup is typically coordinated above the expected starting/inrush current, with appropriate margin and manufacturer-specific tolerances, while remaining sensitive enough to clear a genuine fault quickly. A capacitor bank's own inrush during energizing plays the same role LRA does for a motor — both need the instantaneous element pushed above a brief, expected transient rather than above steady running current alone.

A −ve tolerance allowance is also built into the practical setting: any breaker's own trip unit and any CT feeding it have a manufacturing tolerance band, and a release calculated exactly at the theoretical minimum can trip early if the real device happens to sit at the negative end of that tolerance. Adding a margin for this negative tolerance, on top of the LRA/inrush margin, is standard practice rather than an optional refinement.

LV release setting for a transformer's LV main (incomer)

A transformer's LV main breaker is a different case entirely — it isn't feeding one piece of equipment, it's the single point every downstream LV feeder passes through, so it must never be the first device to trip for a fault that a downstream feeder should clear on its own. Instantaneous protection may need to be restrained or coordinated differently here so that downstream devices have an opportunity to clear their faults first; the actual setting depends on the breaker, system fault level, and selectivity requirements. The general aim is for the LV main's own time-current curve to sit above every downstream feeder's curve at any current level the main could realistically see, giving every downstream breaker a genuine chance to clear its own fault first.

Two approaches are used to size this setting, depending on how well the downstream loads are known at design time:

Approach A — based on known, fixed downstream loads: when every feeder the LV main serves is already defined and no further loads are planned, the main's pickup can be based directly on the actual combined demand of those known feeders (their added FLAs, with margin), and its curve graded to sit above each feeder's own curve. This gives a tightly-matched setting, but it needs revisiting if a new feeder is added later.

Approach B — based on the transformer's own rating: when the downstream load picture isn't fully fixed, or future feeders are expected, the LV main is instead sized against the transformer's own full-load current rating (with a design margin, commonly in the 1.25–1.5× range) rather than against today's actual connected load. This keeps the main's setting valid even as feeders are added or changed later, at the cost of being somewhat less tightly matched to present-day load than Approach A.

Bus coupler consideration: where two transformer-fed LV buses can be tied together through a bus coupler (for standby/parallel operation), the coupler's own release is set with reference to whichever of the two buses carries the heavier load, since that's the worst-case current the coupler itself could be asked to carry, and its curve needs to be graded to sit between the individual feeder curves and the transformer LV main curves on both sides of the tie.

Ground (earth) fault at LV: the same FLA/LRA-based thinking extends to the ground-fault element, but typically set more sensitively (a lower pickup than the phase-overcurrent element) since a ground fault path often carries less current than a bolted phase fault, yet still represents a genuine safety and equipment-damage risk that benefits from faster, more sensitive detection than the phase elements alone would provide.

HV/MV relay setting concepts

Moving further upstream, HV/MV protection is handled by a relay reading current through a CT rather than a breaker's own built-in release, and the relay issues the trip command to a separate breaker. Two broad time-current characteristic families are used: IDMT (Inverse Definite Minimum Time — the family this calculator's Standard Inverse curve belongs to, where operating time shortens automatically as fault current rises) and DMT (Definite Minimum Time — a fixed time delay applied once current exceeds pickup, independent of how far above pickup the actual fault current sits). DMT trades away the automatic speed-up of IDMT for a simpler, purely time-graded coordination scheme, which some coordination schemes prefer for predictability between successive relays.

Instantaneous (element "50") protection for a motor at HV/MV: conceptually mirrors the LV motor release case — set above the motor's starting current with margin, but low enough to clear a genuine terminal or winding fault quickly, since a motor fault left to clear only on the slower IDMT curve risks more severe damage the longer it's allowed to persist.

Instantaneous ("50") protection for a transformer: the connected-load-based versus rating-based split described above for the LV main is a useful conceptual starting point for scaling the setting, but it is not the whole picture — a transformer's actual instantaneous/high-set setting also has to account for inrush current on energization, the transformer's own impedance and through-fault withstand, CT characteristics, any differential protection already covering the transformer, downstream coordination, and breaker interrupting capability. Treat the two-approach split as a starting scale for the setting, not a complete determination of it.

Through-fault current: this is the fault current that flows through a transformer for a fault occurring beyond it (typically on its LV side) rather than inside the transformer's own winding. A transformer's HV-side protection setting has to be checked against this figure specifically, since the transformer must be able to carry that current, undamaged, for however long it takes downstream/LV protection to clear the external fault, before the HV relay's own instantaneous element would otherwise operate unnecessarily for a fault that isn't even inside the transformer's own protected zone.

Earth fault protection at HV/MV: typically senses the residual (zero-sequence) current directly, either through a dedicated core-balance CT or via the residual connection of three phase CTs, and is set well below the phase overcurrent pickup — earth faults at HV/MV are frequently lower in magnitude than a bolted three-phase fault, so a phase-current-only setting would be far too insensitive to reliably detect them.

RMU (Ring Main Unit) relay setting: in ring-operated distribution arrangements such as an RMU, fault-current contribution can depend on the network's specific configuration and current operating state — current may arrive through the associated transformer from the LV side, along the HV ring itself, or both, depending on how the ring is normally run and switched. Protection settings for an RMU should be based on the relevant supply paths for that specific arrangement and operating state, rather than assuming a single fixed direction of fault current flow applies to every ring topology.

Combining multiple transformers on a common HV bus: where several transformers feed a shared HV incomer protected by one upstream relay, two related but distinct ideas come into play. For the normal-load-based (overcurrent) pickup, the relevant current is the sum of every individual transformer's full-load current, since that's what actually flows through the common point under normal operation. For the instantaneous element, the relevant current is instead the largest single transformer's own through-fault contribution, added to the normal full-load current the remaining transformers continue to contribute — representing the realistic worst-case total the upstream relay would see for an internal fault on the biggest unit while the others keep serving their own load.

Coordination discrimination — LV versus HV/MV

The two ends of the chain are also graded differently. At LV, successive breakers are typically checked using manufacturer time-current curves and selectivity data together — not the curves in isolation — since real selectivity also depends on breaker tolerances, any instantaneous or short-time overrides, and manufacturer-published selectivity tables for specific breaker combinations; the underlying principle is still ensuring a genuine current-axis gap between one breaker's curve and the next at every relevant current level, not simply a fixed time step. At HV/MV, by contrast, both time and current discrimination matter together, and a deliberate minimum time step — the Coordination Time Interval (CTI) — is added between each pair of relays in the chain (commonly cited in the few-hundred-millisecond range, with IEEE 242, the "Buff Book," as a widely referenced source for how it's derived) to absorb real-world breaker interrupting time, relay overshoot, and CT/relay tolerance, so the downstream relay reliably finishes clearing the fault before the upstream relay's own delay elapses.

None of this changes the single-relay IDMT calculation this page performs — it's the broader context that calculation sits inside. A relay setting that's correct in isolation still needs to be checked against the LV and HV/MV coordination principles above, and against the actual settings of every adjacent device, before it's finalized for a real installation.

1. Setting pickup current too close to normal maximum load. Without adequate margin (commonly 1.25-1.3× as a starting point, not a fixed rule), normal load fluctuation or a brief legitimate overload can cause nuisance tripping — but too much margin reduces sensitivity to genuine, moderate overload conditions, so this margin needs deliberate, informed selection based on the actual application, not an arbitrary large number.

2. Confusing CT secondary current with CT primary current in the pickup calculation. Plug setting percentage is based on the relay's rated current (referenced to CT secondary, typically 1A or 5A), but load and fault currents are usually known in primary (actual system) amps — keep clear which side of the CT ratio you're working on at each step of the calculation.

3. Calculating TMS using an inconsistent curve type from what the physical relay is actually set to. The k and α constants differ between Standard Inverse, Very Inverse, and Extremely Inverse curves — calculating a TMS value using Standard Inverse constants, then setting a relay actually configured for Very Inverse, gives a wrong and uncoordinated result.

4. Setting a single relay's parameters without checking coordination with adjacent devices. A relay correctly calculated in isolation can still create a coordination problem if it doesn't operate with adequate time margin relative to devices upstream and downstream — a complete protection study checks operating times across the whole system for a range of fault locations and magnitudes, not just one relay's own settings.

5. Using an unrealistic or unverified fault current figure. The PSM (and therefore the resulting TMS calculation) depends entirely on the fault current value used — using an outdated, assumed, or poorly-sourced fault current figure (rather than one confirmed via an actual fault current study) undermines the validity of the entire settings calculation.

6. Assuming a calculated exact TMS value is directly settable, or always rounding to the nearest step without thinking about direction. Real relays offer TMS in discrete steps (commonly 0.05 or 0.1 increments, though numerical relays often allow finer resolution) — rounding down gives a faster trip, rounding up adds coordination margin, and which one is appropriate depends on the specific coordination requirement, not a fixed rule. Always verify the resulting actual operating time with whichever step you select, not just the theoretically calculated exact value.

7. Mixing IEC and ANSI/IEEE curve formula families. These reference standards use different constants and sometimes different curve-shape conventions for nominally similar curve names — confirm which family your relay and coordination study actually use, and don't apply one family's formula to a relay configured for the other.

8. Not providing adequate coordination time interval between successive relays. A coordinated pair of relays needs a real time margin (a commonly cited illustrative range of 0.2-0.4 seconds, though the appropriate value depends on breaker clearing time, relay overshoot, and CT/relay tolerances) between their operating times for the same fault, not just a marginally different TMS — too small a margin risks both relays operating together during real-world timing variation, defeating the purpose of coordination.