Industrial Instrumentation, Metrology & Process Control
Callendar-Van Dusen Pt100 RTD Resistance Formula
Calculate IEC 60751 Platinum RTD Resistance R(T) = R_0 * (1 + A*T + B*T^2) for T >= 0 °C, compare against Naive Linear Alpha (0.00385/°C) Approximation, and quantify Uncalibrated Temperature Drift (°C).
Eliminate +3 °C process-control bias above 100 °C with IEC 60751 Callendar-Van Dusen!
Platinum Resistance Temperature Detectors (Pt100 / Pt1000 RTDs) are the gold standard for pharmaceutical autoclaves, chemical reactors, and semiconductor bake plates. PLC programmers who hardcode the nominal two-point DIN alpha slope R_lin(T) = R_0 * (1 + 0.00385 * T) introduce severe systematic error at elevated temperatures because platinum’s temperature coefficient bends downward quadratically! Under IEC 60751 (for 0 °C <= T <= 850 °C), the Callendar-Van Dusen equation specifies R_CVD(T) = R_0 * (1 + A * T + B * (T ^ 2)) with A = 3.9083 * 10^-3 °C^-1 and B = -5.775 * 10^-7 °C^-2 (which passes identically through 138.5055 Ohm at T = 100 °C while bending below the secant line above 100 °C)!
Verify in a metrology calibration workbook—Ice_Point_Resistance R_0 = 100.00 Ohm (Pt100, B2), Process_Temperature T = 200 °C (B3), IEC_Linear_Coeff A = 0.0039083 (B4), and IEC_Quadratic_Coeff B = -0.0000005775 (B5): Exact IEC 60751 Resistance is 100 * (1 + 0.78166 - 0.02310) = 175.856 Ohm (E2); Naive 0.00385/°C Linear Estimate predicts 100 * (1 + 0.77) = 177.000 Ohm (E3); Resistance Discrepancy is +1.144 Ohm (E4); which translates to a +2.97 °C temperature reading error (1.144 / 0.385 in E5) if a PLC lacks quadratic linearization!
| IEC 60751 Pt100 RTD Metric (R0=100 Ohm, T=200 °C, A=3.9083e-3, B=-5.775e-7) | Formula | Verified Output |
|---|---|---|
| Exact Callendar-Van Dusen R (Ohm) | R_0 * (1 + A * T + B * T^2) | 175.856 Ohm (247.092 @ 400 °C) |
| Naive 0.00385 Linear R_lin (Ohm) | R_0 * (1 + 0.00385 * T) | 177.000 Ohm (254.000 @ 400 °C) |
| Linearization Resistance Bias | R_lin - R_CVD | +1.144 Ohm (0.000 @ 0 °C) |
| Approximate Temperature Error (°C) | (R_lin - R_CVD) / (0.00385 * R_0) | +2.97 °C Uncalibrated Drift |
IEC 60751 Callendar-Van Dusen RTD Resistance (0 to 850 °C) Formula
Validate R_0 > 0, valid positive-branch temperature range 0 <= T <= 850 °C (sub-zero temperatures add the fourth-degree Van Dusen C*(T - 100)*T^3 term!), A > 0, and B < 0!
=LET(r_0, B2, tp_c, B3, cf_a, B4, cf_b, B5, IF(OR(r_0 <= 0, tp_c < 0, tp_c > 850, cf_a <= 0, cf_b >= 0), "Out of Positive CVD Range (0-850C)", ROUND(r_0 * (1 + cf_a * tp_c + cf_b * (tp_c ^ 2)), 3)))400 °C Quadratic Curvature Growth & 0 °C Ice-Point Identity Checks
Double T from 200 °C to 400 °C in B3: Callendar-Van Dusen gives 247.092 Ohm (whereas linear 0.00385 predicts 254.000 Ohm—quadrupling quadratic curvature!). Set T = 0 °C: both CVD and linear equations meet at 100.000 Ohm with 0.00 °C error!
=IF(ISTEXT(E2), E2, ROUND((E3 - E2) / (0.00385 * B2), 2))Try the example
Use the original values or change them to test your understanding.