Temperature Sensor Response Time Calculator
Temperature sensors and thermowells respond like a first order lag. See what a sensor reads at any time after a step change, and its T50, T63, T90 and T99 times.
- T(t) = T0 + (T∞ − T0) × (1 − e−t/τ) = 91.35 °C
Response times
| Response | Multiple of τ | Time |
|---|---|---|
| T50 | 0.693 τ | 5.545 s |
| T63 | 1.000 τ | 8 s |
| T90 | 2.303 τ | 18.42 s |
| T95 | 2.996 τ | 23.97 s |
| T99 | 4.605 τ | 36.84 s |
First Order Response
Tx% = −τ × ln(1 − x/100)
Worked example
A sensor with τ = 8 s, stepped from 20 to 120 °C, reads 91.3 °C after 10 s and reaches 90 % of the step after 18.4 s.
Frequently Asked Questions
What is the time constant of a temperature sensor?
The time to reach 63.2 % of a step change. It depends on the sensor, thermowell, fluid and velocity.
What is T90 response time?
The time to reach 90 % of a step change, 2.3 times the time constant for a first order sensor.
Why does response time matter for control?
Slow sensors add lag to the loop, forcing slower controller tuning and allowing larger overshoot.
Learn more on the blog
Thermocouple and RTD installation precautions
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
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