Mathematics · Geometry
Geodetic Spherical Arc Distance adopted spherical Earth radius Solver
Rearrange the geodetic spherical arc distance relationship and solve for adopted spherical earth radius.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use a=180c/(πb) with surface arc distance=889.5594131564699 and central angle in degrees=8.
- adopted spherical Earth radius=6371.
- Substitution into c=πab/180 reconstructs 889.5594131564699.
Understand Geodetic Spherical Arc Distance: solve adopted spherical Earth radius
One idea, three depths
Choose how deeply to explain Geodetic Spherical Arc Distance: solve adopted spherical Earth radius
Geodetic Spherical Arc Distance: solve adopted spherical Earth radius: Rearrange the geodetic spherical arc distance relationship and solve for adopted spherical earth radius.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Geodetic Spherical Arc Distance: solve adopted spherical Earth radius to answer this question: rearrange the geodetic spherical arc distance relationship and solve for adopted spherical earth radius? Enter surface arc distance and central angle in degrees; the calculator shows adopted spherical Earth radius. For example: adopted spherical Earth radius=6371 and central angle in degrees=8 produce surface arc distance=889.5594131564699. The answer tells you adopted spherical Earth radius.
Age 15Explain it to a 15-year-oldConnect it to the formula
A spherical surface arc equals adopted radius multiplied by central angle expressed in radians. This page isolates adopted spherical earth radius and verifies it in the original relationship. The rule is a=180c/(πb). Its input values are surface arc distance, central angle in degrees, and the main result is adopted spherical Earth radius. For example: adopted spherical Earth radius=6371 and central angle in degrees=8 produce surface arc distance=889.5594131564699.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated geodetic spherical arc distance: solve adopted spherical earth radius relation over the valid real-number domain stated below. The implemented relation is a=180c/(πb), evaluated from surface arc distance, central angle in degrees to produce adopted spherical Earth radius. A spherical surface arc equals adopted radius multiplied by central angle expressed in radians. This page isolates adopted spherical earth radius and verifies it in the original relationship. A reference ellipsoid, geodesic algorithm, height, datum, and longitude wrapping are required when spherical approximation error is material.
Inputs and valid domain
- surface arc distance must be a finite real number.
- central angle in degrees must be a finite real number.
Important boundary: A reference ellipsoid, geodesic algorithm, height, datum, and longitude wrapping are required when spherical approximation error is material.
The formula
a=180c/(πb)
How the calculator works through it
It substitutes surface arc distance, central angle in degrees into the formula and exposes every numerical step above. The main output is adopted spherical Earth radius, accompanied by Reconstructed surface arc distance.
Read the result correctly
The adopted spherical Earth radius is the direct answer to “rearrange the geodetic spherical arc distance relationship and solve for adopted spherical earth radius.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
adopted spherical Earth radius=6371 and central angle in degrees=8 produce surface arc distance=889.5594131564699.
Where this model stops being reliable
A reference ellipsoid, geodesic algorithm, height, datum, and longitude wrapping are required when spherical approximation error is material.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Geodetic Spherical Arc Distance: solve adopted spherical Earth radius works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Geodetic Spherical Arc Distance: solve adopted spherical Earth radius uses a=180c/(πb). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Ratios between measured quantities
Ratios help you check the scale, units and proportional meaning of Geodetic Spherical Arc Distance: solve adopted spherical Earth radius.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Geodetic Spherical Arc Distance: solve adopted spherical Earth radius to related shapes and constructions.
Review this foundation about 4 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read surface arc distance, central angle in degrees.
- Evaluate the principal relationship: a=180c/(πb).
- Return adopted spherical Earth radius and check the domain conditions described above.
Python
from math import *
def geodetic_spherical_arc_distance_solve_a(c, b) -> float:
return ((c * 180.0) / (pi * b))
assert abs(geodetic_spherical_arc_distance_solve_a(889.5594131564699, 8) - 6371) < 1e-6 * max(1.0, abs(6371))
C
#include <assert.h>
#include <math.h>
double geodetic_spherical_arc_distance_solve_a(double c, double b) {
return ((c * 180.0) / (3.141592653589793 * b));
}
int main(void) {
const double expected = 6371;
const double actual = geodetic_spherical_arc_distance_solve_a(889.5594131564699, 8);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double geodetic_spherical_arc_distance_solve_a(double c, double b) {
return ((c * 180.0) / (std::numbers::pi * b));
}
int main() {
constexpr double expected = 6371;
const double actual = geodetic_spherical_arc_distance_solve_a(889.5594131564699, 8);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double geodetic_spherical_arc_distance_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global geodetic_spherical_arc_distance_solve_a
section .text
geodetic_spherical_arc_distance_solve_a:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4066800000000000
movq xmm0, rax
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
mov rax, 0x400921fb54442d18
movq xmm0, rax
movsd [rbp-56], xmm0
movsd xmm0, [rbp-56]
mulsd xmm0, [rbp-16]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-32]
divsd xmm0, [rbp-48]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = geodetic_spherical_arc_distance_solve_a(c, b)
result = ((c * 180.0) / (pi * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, b_] := ((c * 180.0) / (Pi * b));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Geodetic Spherical Arc Distance adopted spherical Earth radius Solver. MW SysArc Tools. https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver
MLA 9
MW SysArc. “Geodetic Spherical Arc Distance adopted spherical Earth radius Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Geodetic Spherical Arc Distance adopted spherical Earth radius Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver.
Harvard
MW SysArc (2026) ‘Geodetic Spherical Arc Distance adopted spherical Earth radius Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_geodetic_spherical_arc_distance_solve_a_2026,
author = {{MW SysArc}},
title = {Geodetic Spherical Arc Distance adopted spherical Earth radius Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Geodetic Spherical Arc Distance adopted spherical Earth radius Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/geodetic-spherical-arc-distance-adopted-spherical-earth-radius-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Geodetic Spherical Arc Distance: solve adopted spherical Earth radius do?
Rearrange the geodetic spherical arc distance relationship and solve for adopted spherical earth radius.
How does the Geodetic Spherical Arc Distance: solve adopted spherical Earth radius work?
The calculator applies a=180c/(πb). A spherical surface arc equals adopted radius multiplied by central angle expressed in radians. This page isolates adopted spherical earth radius and verifies it in the original relationship.
What can I learn from the Geodetic Spherical Arc Distance: solve adopted spherical Earth radius?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .