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.
