HP 20S: The July 2026 Program Collection
Triangulation
d = l * sin(α) * sin(ß) ÷ sin(α + ß)
Store in the following registers before calculation:
R1 = measure of angle A
R2 = measure of angle B
R3 = length l from point A to B
Solve:
R4: distance
Code:
01: LBL A; 61, 41 ,A
02: DEG; 61, 23
03: RCL 1; 22, 1
04: SIN; 23
05: ×; 55
06: RCL 2; 22, 2
07: SIN; 23
08: ÷; 45
09: (; 33
10: RCL 1; 22, 1
11: +; 75
12: RCL 2; 22, 2
13: ); 34
14: SIN; 23
15: ×; 55
16: RCL 3; 22, 3
17: =; 74
18: STO 4; 21, 4
19: RTN; 61, 26
Examples
Example 1:
Inputs: R1 = 60°, R2 = 50°, R3 = 10
Output: R4: 7.05990377592
Example 2:
Input: R1 = 30°, R2 = 80°, R3 = 27.5
Output: R4: 14.4101446626
Source:
“Triangulation (surveying)” Wikipedia. https://en.wikipedia.org/wiki/Triangulation_(surveying) (last edited October 24, 2025). Retried March 17, 2026
Payment: Continuous Compounding
PMT = PV * (e^r – 1) ÷ (1 – e^(-r * t))
Store in the following registers before calculation:
R1 = t: number of payments
R2 = r: periodic interest rate (as a decimal)
R3 = PV: present value
Solve:
R4: PMT: present
Code:
01: GTO B; 61, 41, b
02: RCL 3; 22, 3
03: ×; 55
04: (; 33
05: RCL 2; 22, 2
06: e^x; 12
07: -; 65
08: 1; 1
09: ); 34
10: ÷; 45
11: (; 33
12: 1; 1
13: -; 65
14: (; 33
15: RCL 1; 22, 1
16: ×; 55
17: RCL 2; 22, 2
18: ); 34
19: +/-; 32
20: e^x; 12
21: ); 34
22: =; 74
23: STO 4; 21, 4
24: RTN; 61, 26
Examples
Example 1:
Input: t: 36, r: 0.10 ÷ 12, PV: 5,000.00
Output: PMT: 161.434037378
Example 2:
Input: t: 60, r: 0.05 ÷ 12; PV: 26,349.56
Output: PMT: 497.374636585
Electrical Engineering: System Temperature to Noise Figure
When an amplifier is activated, two ways to express noise are the noise temperature (in Kelvin) and the noise figure (in decibels, dB). Using a reference temperature of 290 K, when the noise temperature (T) is known, the noise figure (F) can be calculated by:
F = 10 * log((T + 290) ÷ 290)
If temperature is given in degrees Celsius (°C), then the formula for noise figure becomes:
F = 10 * log((T°C + 563.15) ÷ 290)
since T = T°C + 273.15.
The following program assumes that temperature is given in degrees Celsius.
Store in the following registers before calculation:
R1 = T°C; temperature in degrees Celsius
Solve:
R2: F: noise figure
Code:
01: LBL C; 61, 41, C
02: RCL 1; 21, 1
03: +; 75
04: 5; 5
05: 6; 6
06: 3; 3
07 . ; 73
08: 1; 1
09: 5; 5
10: =; 74
11: ÷; 45
12: 2; 2
13: 9; 9
14: 0; 0
15: =; 74
16: LOG; 51, 13
17: ×; 55
18: 1; 1
19: 0; 0
20: =; 74
21: STO 2; 21, 2
22: RTN; 61, 26
Examples
Example 1:
Input: T = -160 °C (store in R1)
Output: F: 1.43068666235 dB
Example 2:
Input: T = 15°C
Output: F: 2.99642532081 dB
Source:
Ball, John A. Algorithms for RPN Calculators John Wiley & Sons: New York. 1978. ISBN 0-47-03070-8. pp. 266-267
Moderate Exercise: Target Heart Rate Range
The following equations calculate the target heart range for a typical person engaging in moderate exercise. According to the particle by Jenna Fletcher (see Source), the American Heart Society (AHA) states the person is engaged in moderate exercise when their heart rate is 50% to 70% of their maximum heart rate. The maximum heart rate is 220 minus the person’s age.
Disclaimer: This is not medical advice, any questions should be discussed with a doctor or health professional.
The moderate range is determined by:
high = (220 – age) * 0.7 = low * 1.4
low = (220 – age) * 0.5 = high * 5/7
For high intensity, use the range 70% to 85%.
Code:
01: LBL D; 61, 41, d
02: +/-; 32
03: +; 75
04: 2; 2
05: 2; 2
06: 0; 0
07: =; 74
08: ÷; 2
09: 2; 2
10: =; 74
11: R/S; 26
12: ×; 55
13: 1; 1
14: . ; 73
15: 4 ; 4
16: =; 74
17: RTN; 61, 26
Examples
Example 1:
Input: Age 49 (my age at the time of this blog)
Output: low: 85.5, high: 119.7
Example 2:
Input: Age 25
Output: low: 97.5, high: 136.5
Source:
Fletcher, Jenna. “What a target heart rate is and how to calculate it”. Medically Reviewed by Debra Sullivan Ph. D. Medical News Today. January 22, 2024. https://www.medicalnewstoday.com/articles/target-heart-rate-calculator March 16, 2026.
Percentile in a Range
The program calculates the percentile of x in the range [a, b].
percentile = (x – a) ÷ (b – a) * 100%
Store before calculating:
R1 = a, R2 = b, R3 = x
Code:
01: LBL E; 61, 42, E
02: ( ; 33
03: RCL 3; 22, 3
04: - ; 65
05 RCL 1; 22, 1
06: ) ; 34
07: ÷; 45
08: ( ; 33
09: RCL 2; 22, 2
10: - ; 65
11: RCL 1; 22, 1
12: ) ; 34
13: ×; 55
14: 2; 2
15: 10^x; 51, 12
16: =; 74
17: RTN; 61, 26
Examples
Example 1:
Input: R1 = 10, R2 = 50, R3 = 30 (30 in [10, 50])
Output: 50 (50%)
Example 2:
Input: R1 = 85.5, R2 = 117.5, R3 = 110 (110 in [85.5, 117.5])
Output: 76.5625 (76.5625%)
Programming all five of these programs will fill the program space of the HP 20S entirely (99 steps)!
Eddie
All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
