NTC Thermistor Temperature Approximation (for HP 42s)

Using Three-coefficient formula using cube root

2026-07-06

Takayuki HOSODA

Usage

Resistance  → Temperature conversion : [SOLVER] [NTCXH] Resistance  [R] [Tc]
Temperature → Resistance conversion  : [SOLVER] [NTCXH] Temperature [Tc] [R]

Variables

MEM "R"  : resistance [Ω]
MEM "Tc" : temperature [°C]

Temperature Approximation Formula for NTC Thermistors

(Hosoda-3)

where,

The component-dependent coefficients a, b, and c in the three-coefficient approximation formula (Hosoda-3) were determined using a computer program to minimize the absolute error within the specified temperature range relative to the median value of each component.

Approximation errors

Program list (HP 42S)

NCPXH — HP 42S Solver program for the Murata NCP15XH103D, Rev.3.0 (2026-07-06)

00 { 80-Byte Prgm }
01>LBL "NCPXH"
02 MVAR "Tc"
03 MVAR "R"
04 RCL "R"
05 10E3
06 ÷
07 LN
08 0.0850436  # coefficient b
09 ×
10 1
11 +
12 1/X
13 1
14 -
15 0.37486    # coefficient a
16 ×
17 1
18 +
19 3
20 1/x
21 Y↑X
22 1
23 -
24 2506.58    # coefficient c
25 ×
26 25
27 +
28 RCL- "Tc"
29 .END.

Download NCPXH — raw program files for the Free42

The coefficients in this example are for the Murata NCP15XH103D (R₂₅ = 10 kΩ). For other NTC thermistors, only the three coefficients (a, b, and c) need to be replaced. Coefficients for several other NTC thermistors are available from the online calculator section .

SEE ALSO

• NTC Thermistor Temperature Approximation Using a Three-Coefficient Cube-Root Formula
• Pt100 - Pt100-1997 Platinum RTD Resistance V.S. Temperature function

HP 42S Program Library

• ABC2XY—Triangulation, tree known distance to the coordinates conversion
• AGM—Arithmetic-Geometric Mean
• AVR—Adjustable voltage regulator (such as LM317 or TL431) solver program
• BPFFL—Center frequency and Q of a Fliege band-pass-filter
• BPFMF—Gain coefficent, center frequency and Q of a multiple-feedback band-pass-filter
• cbrt—Cube root function
• E24—Find nearest fraction(s) in the E24 numbers
• eW—exponent of Lambert W function
• Factr—Factor a positive integer
• Frac—Fractional approximation
• LCM/GCD—LCM and GCD of two positive integers
• LCR—Resonant frequency of a LC resonator
• LPFMF—Gain coefficent, center frequency and Q of a multiple-feedback low-pass-filter
• L•—Inductanse of a straight conductor of circular section
• L-—Inductanse of a straight conductor of thin flat section
• NCPXH—NTC thermistor temperature/resistance function for the HP 42S Solver
• OST—SOLVE alternative, numerical solution of a lenear equation using Ostrowski's method
• RI—Rational interpolation
• Pt100—Pt100-1997 Temperature V.S. Resistance function to solve
• μZw, μwZ—Synthesize/Analyze microstrip transmission line
• cbcpw—Analyze Conductor-backed Coplanar Wave guide / Complete elliptic integral of the first kind K(k)
• Vn—Input refered voltage noise of an operational amplifier
• Z→S—Impedance Z to S₁₁ scattering parameter conversion
• ZdSL—Differential impedance of an edge coupled stripline solver program