PT100 / PT1000 Calculator
RTD resistance ↔ temperature per IEC 60751 (Callendar-Van Dusen).
R(T) = R0·(1 + A·T + B·T²)
A = 3.9083×10⁻³ · B = −5.775×10⁻⁷
This tool converts platinum RTD resistance to temperature and back for PT100 and PT1000 sensors, using the IEC 60751 Callendar-Van Dusen equation over 0…850 °C. Reference points: 100 °C ↔ 138.5055 Ω, and a measured 108.5 Ω ↔ 21.8189 °C on a PT100.
How it works
Platinum resistance rises almost — but not exactly — linearly with temperature. IEC 60751 captures the curvature with R(T) = R0·(1 + A·T + B·T²) for T ≥ 0 °C, where A = 3.9083×10⁻³ and B = −5.775×10⁻⁷. Because that is a quadratic in T, the reverse direction has a closed-form solution via the quadratic formula — this calculator uses it directly, so resistance → temperature → resistance round-trips to within 10⁻⁵ Ω.
The negative branch of the standard (with its additional C coefficient) is intentionally not implemented; out-of-range inputs are refused with the supported range stated.
Worked example
R = 100 × (1 + 3.9083×10⁻³·100 − 5.775×10⁻⁷·100²)
= 138.5055 Ω
measured R = 108.5 Ω → T = 21.8189 °C
Parameters
| Parameter | Value | Notes |
|---|---|---|
| Standard | IEC 60751 | Callendar-Van Dusen |
| A | 3.9083 × 10⁻³ °C⁻¹ | |
| B | −5.775 × 10⁻⁷ °C⁻² | |
| R0 | 100 Ω (PT100) / 1000 Ω (PT1000) | |
| Range | 0 … 850 °C | T < 0 branch (C term) not implemented |
Python implementation
# IEC 60751 Callendar-Van Dusen, T >= 0 °C
A, B = 3.9083e-3, -5.775e-7
def rtd_resistance(t, r0=100.0):
return r0 * (1 + A*t + B*t*t)
def rtd_temperature(r, r0=100.0):
return (-A + ((A*A - 4*B*(1 - r/r0)) ** 0.5)) / (2*B)
assert abs(rtd_resistance(100) - 138.5055) < 1e-3
assert abs(rtd_temperature(108.5) - 21.8189) < 1e-3FAQ
▸Which equation and coefficients are used?
The IEC 60751 Callendar-Van Dusen equation for T ≥ 0 °C: R(T) = R0·(1 + A·T + B·T²), with A = 3.9083×10⁻³ and B = −5.775×10⁻⁷. Temperature from resistance is the exact quadratic inverse, not a lookup-table approximation.
▸Why is the range limited to 0…850 °C?
Below 0 °C the standard adds a C-term quartic, a different equation branch that this calculator does not yet implement. Above 850 °C is outside the IEC 60751 platinum range. Inputs outside the supported range are rejected explicitly rather than silently extrapolated.
▸What is the difference between PT100 and PT1000?
Only R0, the resistance at 0 °C: 100 Ω versus 1000 Ω. The temperature coefficients are identical, so a PT1000 reads exactly ten times the resistance of a PT100 at every temperature — 1385.055 Ω instead of 138.5055 Ω at 100 °C.
▸My meter shows 108.5 Ω on a PT100 — what temperature is that?
21.8189 °C. A handy field rule: near room temperature a PT100 changes by roughly 0.39 Ω per °C, so 108.5 Ω sits about 22 °C above the 100 Ω ice point — the exact quadratic confirms it.
▸Is my data uploaded?
No. The equation is evaluated locally in your browser.
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