When configuring solid-state time-delay relays for motor starters, HVAC blower circuits, or lighting contactors, guessing the dial position leads to nuisance trips and failed star-delta transitions. A T100 calculator removes the guesswork by mapping the physical potentiometer dial position to a precise time delay using the linear scaling formula. The direct answer for any standard linear T100-series timer is: Tdelay = Trange × (D / 100). Below is the complete derivation, unit tracking, and bench-verification data you need to set your relays correctly on the first try.

The Core T100 Timing Formula and Symbol Definitions

The T100 series of time-delay relays (encompassing popular DIN-rail models from manufacturers like Macromatic, Schneider, and generic equivalents) relies on an internal RC (resistor-capacitor) timing circuit. The external potentiometer (the dial) varies the resistance, scaling the maximum time range set by the internal DIP switches or terminal jumpers.

When this formula applies: This linear scaling formula applies specifically to modern solid-state T100 timers with a linear-taper potentiometer operating in On-Delay, Off-Delay, Interval, or Repeat Cycle modes. It assumes a stable control voltage (e.g., 24VDC or 120VAC ±10%) and an ambient temperature between 0°C and 50°C.

Formula and Symbol Table

Tdelay = Trange × (D / 100)

SymbolDefinitionStandard Unit
TdelayThe actual target time delay before the relay contacts change state.Seconds (s) or Minutes (min)
TrangeThe maximum time range selected via the relay's DIP switch or jumper block.Seconds (s) or Minutes (min)
DThe physical dial setting, read as a percentage of the full scale (0 to 100).Percent (%)
TtolFactory tolerance factor, typically ±5% of the calculated Tdelay.Seconds (s)

Rearranged Forms for Every Variable

On the jobsite, you rarely need to find Tdelay from scratch; usually, you know the delay you need and must find the dial setting. Here are the algebraic rearrangements for every variable in the T100 calculator formula:

  • Solve for Dial Setting (D): D = (Tdelay / Trange) × 100
  • Solve for Required Range (Trange): Trange = Tdelay / (D / 100)
  • Solve for Actual Delay (Tdelay): Tdelay = Trange × (D / 100)
  • Calculate Maximum Tolerance Bound: Tmax = Tdelay + (Tdelay × 0.05)
  • Calculate Minimum Tolerance Bound: Tmin = Tdelay - (Tdelay × 0.05)

Worked Examples with Unit Tracking

Abstract formulas don't wire panels. Here are two real-world scenarios with strict unit tracking to demonstrate how the T100 calculator operates in practice.

Problem 1: HVAC Blower Off-Delay

Scenario: You are wiring an HVAC air handler. The thermostat calls for cooling to stop, but you need the blower motor to run for exactly 45 seconds to extract residual cold air from the ductwork. Your T100 off-delay relay has its DIP switches set to a 0–60 second range.

  1. Identify Knowns: Tdelay = 45 s; Trange = 60 s.
  2. Select Formula: D = (Tdelay / Trange) × 100.
  3. Substitute Values: D = (45 s / 60 s) × 100.
  4. Calculate: D = 0.75 × 100 = 75%.
  5. Determine Tolerance Bounds: 5% of 45 s = 2.25 s. Acceptable window is 42.75 s to 47.25 s.

Result: Turn the potentiometer dial to the 75% mark (often indicated by a '7.5' on a 0-10 scale). Verify with a stopwatch that the contacts open between 42.7 and 47.2 seconds after the trigger signal drops.

Problem 2: Motor Star-Delta Transition

Scenario: You are commissioning a 50HP 3-phase motor using a star-delta starter. The transition from star (reduced voltage) to delta (full voltage) must occur at 3.5 seconds to prevent the upstream 100A breaker from tripping on inrush current. Your T100 on-delay relay is configured for a 0–10 second range.

  1. Identify Knowns: Tdelay = 3.5 s; Trange = 10 s.
  2. Select Formula: D = (Tdelay / Trange) × 100.
  3. Substitute Values: D = (3.5 s / 10 s) × 100.
  4. Calculate: D = 0.35 × 100 = 35%.
  5. Determine Tolerance Bounds: 5% of 3.5 s = 0.175 s. Acceptable window is 3.325 s to 3.675 s.

Result: Set the dial to 35%. Because star-delta transitions are highly sensitive to timing, if your bench test yields 3.7 seconds, dial it back to 32% to compensate for the specific unit's positive tolerance drift.

Unit Mistakes That Break the Calculation

The math is simple; the unit conversions are where technicians fry contactors. Avoid these three critical mistakes:

Mistake 1: Mixing Minutes and Seconds on the DIP Switch
If your target Tdelay is 90 seconds, and you leave the DIP switch on the '10 Minutes' (600s) range, your dial calculation becomes D = (90 / 600) × 100 = 15%. Setting a dial to 15% is highly inaccurate due to the mechanical dead-band at the bottom of the potentiometer track. Fix: Always select the tightest Trange that encompasses your Tdelay (e.g., use the 100s range, yielding a 90% dial setting).

Mistake 2: Assuming Logarithmic Dials are Linear
While modern T100 relays use linear-taper potentiometers, some legacy or specialized high-range timers use logarithmic tapers to allow fine-tuning at low durations. If your datasheet specifies a log taper, the linear T100 calculator formula will yield wildly incorrect results at the extremes of the dial. Always verify the taper type in the manufacturer's datasheet.

Mistake 3: Ignoring the Flyback Diode Delay
The T100 calculator gives you the electronic timing of the internal solid-state circuit. However, if you are driving a DC mechanical contactor coil and have installed a flyback diode (like a 1N4007) across the coil to suppress voltage spikes, the magnetic field collapse is slowed. This can add 15ms to 50ms of physical dropout time that the T100 calculator cannot predict.

Decision Path: Selecting the Right T100 Relay and Setting

Use this decision tree to select the correct base range and terminate in a concrete hardware pick for standard industrial control panels.

Condition (Target Delay)Action (DIP / Jumper Setting)Resulting Dial Target
If Tdelay < 1.0 secondSet Range to 1.0s (or 0.1s-1s)Dial > 10% (Avoids dead-band)
If Tdelay is 1.0s to 10.0sSet Range to 10.0sDial 10% to 100%
If Tdelay is 10s to 60sSet Range to 60.0sDial 16% to 100%
If Tdelay > 60 secondsSet Range to 100 Minutes; convert Tdelay to minDial calculated in minutes

Concrete Hardware Pick: For 90% of 24V DC control circuits requiring adjustable on/off delays between 0.1s and 100 hours, specify the Macromatic T100-2040-24 (24V AC/DC, 10A SPDT, DIN-rail mount). It features a true linear potentiometer, making the T100 calculator formula perfectly accurate across its entire range, and conforms to IEC 61812-1 standards for time relays.

Realistic Answer Magnitudes and Bench Verification

What does a 'correct' answer actually look like on the bench? If you calculate a 5.0-second delay and set your dial to 50% on a 10s range, you should not expect a perfect 5.000s trip.

Realistic Magnitudes:
Due to the ±5% factory tolerance on the internal timing capacitor and the ±1% tolerance on the cermet potentiometer track, a calculated 5.0s delay will realistically measure between 4.75s and 5.25s when captured on an oscilloscope or a PLC high-speed counter.

Bench Verification Protocol:

  1. Wire a 24VDC indicator lamp to the relay's NO (Normally Open) contact.
  2. Apply the trigger signal and start a digital stopwatch simultaneously.
  3. Stop the watch the exact millisecond the lamp illuminates.
  4. Repeat three times. If the average falls outside your calculated Tmin and Tmax bounds, the internal timing capacitor may be suffering from dielectric absorption (common in units stored for >3 years). Cycle the relay through 10 rapid 1-second intervals to 'reform' the capacitor, then re-test.

By treating the T100 calculator not just as a math exercise, but as a baseline for physical bench verification, you eliminate the trial-and-error dial twisting that plagues control panel commissioning. Set the range tight, calculate the percentage, and verify with a timer.