Earth's Radius by Latitude
Introduction: Calculating the Earth’s Radius
In quick, general calculations, we assume that the shape of the Earth approximates the shape of sphere, with the radius to generally be approximated as 6371 km. However, the shape of the Earth is closer to an oblate ellipsoid. The Earth is flattened at the poles and bulges the greatest at the Equator.
There are several calculations to estimate the Earth’s radius given the latitude (degrees North or South from the Equator), this blog is working with the WGS 84 formula (see Source):
R = √[ ((a² * cos(φ))² + (b² * sin(φ))²) ÷ ((a * cos(φ))² + (b * sin(φ))²) ]
Which is simplified from:
R = √[ (a^4 + b^4 * tan²(φ)) ÷ (a² + b² * tan²(φ))
where:
φ: latitude (in degrees)
a: semi-major axis: 6378.137 km
b: semi-minor axis: 6356.7523142 km
R: radius of kilometers
HP 15C Code: Earth’s Radius by Latitude
Step; Key; Key Code
001: LBL E; 42, 21, 15
002: DEG; 43, 7
003: →H; 43, 2
004: TAN; 25
005: x²; 43, 11
006: STO 1; 44, 1
007: 6; 6
008: 3; 3
009: 7; 7
010: 8; 8
011: . ; 48
012: 1; 1
013: 3; 3
014: 7; 7
015: STO 2; 44, 2
016: 4; 4
017: 14; y^x
018: 6; 6
019: 3; 3
020: 5; 5
021: 6; 6
022: . ; 48
023: 7; 7
024: 5; 5
025: 2; 2
026: 3; 3
027: 1; 1
028: 4; 4
029: 2; 2
030: STO 3; 44, 3
031: 4; 4
032: y^x; 14
033: RCL 1; 45, 1
034: ×; 20
035: +; 40
036: RCL 2; 45, 2
037: x²; 43, 11
038: RCL 3; 45, 3
039: x²; 43, 11
040: RCL 1; 45, 1
041: ×; 20
042: +; 40
043: ÷; 10
044: √; 11
045: RTN; 43, 32
TI-60 Code: Earth’s Radius by Latitude
Step; Key; Key Code
Set degrees mode before beginning.
00: DMS-DD; 39
01: TAN; 34
02: x²; 96
03: STO; 61
04: 1; 01
05: ( ; 53
06: 6; 06
07: 3; 03
08: 7; 07
09: 8; 08
10: . ; 93
11: 1; 01
12: 3; 03
13: 7; 07
14: STO; 61
15: 2; 02
16: y^x; 45
17: 4; 04
18: +; 85
19: 6; 06
20: 3; 03
21: 5; 05
22: 6; 06
23: . ; 93
24: 7; 07
25: 5; 05
26: 2; 02
27: 3; 03
28: 1; 01
29: 4; 04
30: 2; 02
31: STO; 61
32: 3; 03
33: y^x; 45
34: 4; 04
35: ×; 25
36: RCL; 71
37: 1; 01
38: ) ; 54
39: ÷; 55
40: ( ; 53
41: RCL; 71
42: 2; 02
43: x²; 96
44: +; 85
45: RCL; 71
46: 3; 03
47: x²; 96
48: ×; 65
49: RCL; 71
50: 1; 01
51: ) ; 54
52: = ; 95
53: √; 86
54: R/S; 13
55: RST; 22
Examples
Latitude: 80° 00’; Radius (km): 6357.402412
Latitude: 57° 24’; Radius (km): 6362.996788
Latitude: 43° 40’; Radius (km): 6367.986902
Latitude: 9° 15’; Radius (km): 6377.588959
Latitude: 2° 56’; Radius (km): 6378.081467
Source
Planetcalc. “Earth Radius by Latitude (WGS 84)” Timur. 2021. https://planetcalc.com/7721/ Retrieved March 22, 2026.
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.
