# Inverse Time Over Current (TOC/IDMT) relay trip time calculator.

The Inverse Time Over Current (TOC/IDMT) relay trip time calculator calculates the protection trip time according to IEC 60255 and IEEE C37.112-1996 protection curves.

## See Also

- Cable Sizing Calculator AS/NZS 3008
- AC and DC Voltage Drop Calculator with Formulas and Examples AS/NZS 3008

## Parameters

**Trip curve**. Select from the standard set of IEC and IEEE curves.**Relay pickup current (A)**. The electrical current pickup set point**I**in the relay._{s}**Fault current (A).**The expected short circuit fault current**I**.**TMS (IEC) or TD (IEEE) setting.**- IEC Time Multiplier Setting (TMS).
- IEEE Time Dial (TD). In some relays a Time Dial Multiplier (TDM) is specified instead of a Time Dial (TD). See conversion here.

## How to convert from Time Dial Multiplier (TDM) to a Time Dial (TD)?

For IEEE curves, convert from a Time Dial Multiplier (TDM) to Time Dial (TD) as follows:

\(TD = 7 \cdot TDM \)

## What is Inverse Time Overcurrent (TOC)?

Inverse Time Over Current (TOC), also referred to as Time Over Current (TOC), or Inverse Definite Minimum Time (IDMT), means that the trip time is inversely proportional to the fault current.

## What is IDMT?

Inverse Definite Minimum Time (IDMT), also referred to as Inverse Time Over Current (TOC), or Time Over Current (TOC), means that the trip time is inversely proportional to the fault current.

## IEC 60255 IDMT (TOC) Trip Curves

The IDMT curve formula to calculate the trip time is:

\(t(I)= TMS \displaystyle \left( \frac {k}{\displaystyle \left(\frac{I}{Is}\right)^\alpha-1}\right)\)

Where:

**I**is the current setting._{s}**I**is the actual current.**k**and**α**are the curve type constants. See table below.

## IEC 60255 equation constants

Curve type | k | α |
---|---|---|

IEC standard inverse curve | 0.140 | 0.020 |

IEC very inverse curve | 13.5 | 1 |

IEC extremely inverse curve | 80 | 2 |

IEC long time standard inverse curve | 120 | 1 |

## IEEE C37.112-1996 IDMT (TOC) Trip Curves

The IDMT curve formula to calculate the trip time is:

\(t(I)= TD \displaystyle \left( \frac {A}{\displaystyle \left(\frac{I}{Is}\right)^p-1}+B\right)\)

Where:

**I**is the current setting._{s}**I**is the actual current.**k**and**α**are the curve type constants. See table below.

As mentioned in parameters, a Time Dial Multiplier (TDM) is sometimes specified by the relay manufacturer instead of a Time Dial (TD). See conversion here.

Curve type | A | B | p |
---|---|---|---|

IEEE moderately inverse curve | 0.0515 | 0.114 | 0.02 |

IEEE very inverse curve | 19.61 | 0.491 | 2 |

IEEE extremely inverse curve | 28.2 | 0.1217 | 2.0 |