Sensor Response Time Calculator (Time Constant, T63, T90)
By Santaji GadepatilinUpdated October 29, 2026
Temperature sensors in thermowells, pressure transmitters with damping and many analysers respond like a first-order lag, reaching 63.2% of a step change in one time constant. This sensor response time calculator converts the time constant into T50, T90 and T99 and predicts the reading at any time — see temperature sensor response time and pressure transmitter damping and response time.
How to use the sensor response time calculator
Enter the sensor’s time constant (the T63.2 value from the datasheet) and a time after a step change. The calculator gives T50, T90 and T99 and the fraction of the step reached. Enter the initial and new process value to see what the sensor reads at that time. To work from a datasheet T90, clear the time constant and enter T90.
First-order response formulas
Reading(t) = T0 + (Tfinal − T0)(1 − e−t/τ)
Tx = −τ × ln(1 − x) · T50 = 0.693 τ · T90 = 2.303 τ · T99 = 4.605 τ
Example
A Pt100 in a thermowell with τ = 8 s; the process jumps from 20 °C to 100 °C:
- T50 = 5.55 s, T90 = 18.42 s, T99 = 36.84 s
- After 10 s: 1 − e−10/8 = 71.35% of the step
- Reading = 20 + 80 × 0.7135 = 77.08 °C
Response time multiples
| Time | Response (% of step) |
|---|---|
| 0.5 τ | 39.3% |
| 1 τ | 63.2% |
| 2 τ | 86.5% |
| 2.303 τ | 90.0% |
| 3 τ | 95.0% |
| 4 τ | 98.2% |
| 4.605 τ | 99.0% |
| 5 τ | 99.3% |
Typical time constants (in water, approximate)
| Sensor | Typical τ |
|---|---|
| Bare 0.5 mm mineral-insulated thermocouple | under 0.5 s |
| 6 mm sheathed Pt100 | 2–5 s |
| Pt100 in a drilled thermowell | 10–60 s |
| Pressure transmitter (no damping) | 0.1–0.3 s |
Response in air or gas is many times slower than in flowing liquid.
Frequently asked questions
What is the time constant of a sensor?
The time to reach 63.2% of a step change, assuming a first-order response. After 5 time constants the sensor has reached 99.3%.
How do I convert T90 to a time constant?
For a first-order sensor, T90 = τ × ln 10 ≈ 2.303 τ, so τ = T90 ÷ 2.303. Enter T90 here and the time constant is solved for you.
Why is my thermowell sensor so slow?
The thermowell wall, air gap and fluid velocity add thermal lag. A spring-loaded sensor tip, thermal paste and a thinner, shorter well all reduce the time constant.
Does transmitter damping add to the response time?
Yes. Damping is a first-order filter with its own time constant; combined with the sensor, the total response is slower than either alone.