Mathematics · Trigonometry
Geodetic Parallel Arc Distance Calculator
Calculate spherical parallel arc distance from equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a cos(b) with equatorial arc distance for the same longitude interval=240 and geocentric latitude magnitude in degrees=52.
- spherical parallel arc distance=147.75875407815798.
Understand Geodetic Parallel Arc Distance
One idea, three depths
Choose how deeply to explain Geodetic Parallel Arc Distance
Geodetic Parallel Arc Distance: Calculate spherical parallel arc distance from equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Geodetic Parallel Arc Distance to answer this question: calculate spherical parallel arc distance from equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees? Enter equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees; the calculator shows spherical parallel arc distance. For example: equatorial arc distance for the same longitude interval=240 and geocentric latitude magnitude in degrees=52 produce spherical parallel arc distance=147.75875407815798. The answer tells you spherical parallel arc distance.
Age 15Explain it to a 15-year-oldConnect it to the formula
On a sphere, an east-west arc along a parallel is the corresponding equatorial arc multiplied by cosine of latitude. This page evaluates the relationship directly. The rule is c=a cos(b). Its input values are equatorial arc distance for the same longitude interval, geocentric latitude magnitude in degrees, and the main result is spherical parallel arc distance. For example: equatorial arc distance for the same longitude interval=240 and geocentric latitude magnitude in degrees=52 produce spherical parallel arc distance=147.75875407815798.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated geodetic parallel arc distance relation over the valid real-number domain stated below. The implemented relation is c=a cos(b), evaluated from equatorial arc distance for the same longitude interval, geocentric latitude magnitude in degrees to produce spherical parallel arc distance. On a sphere, an east-west arc along a parallel is the corresponding equatorial arc multiplied by cosine of latitude. This page evaluates the relationship directly. Geodetic versus geocentric latitude, ellipsoidal radius of curvature, datum, height, and antimeridian handling affect real geodetic work.
Inputs and valid domain
- equatorial arc distance for the same longitude interval must be a finite real number.
- geocentric latitude magnitude in degrees must be a finite real number.
Important boundary: Geodetic versus geocentric latitude, ellipsoidal radius of curvature, datum, height, and antimeridian handling affect real geodetic work.
The formula
c=a cos(b)
How the calculator works through it
It substitutes equatorial arc distance for the same longitude interval, geocentric latitude magnitude in degrees into the formula and exposes every numerical step above. The main output is spherical parallel arc distance.
Read the result correctly
The spherical parallel arc distance is the direct answer to “calculate spherical parallel arc distance from equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
equatorial arc distance for the same longitude interval=240 and geocentric latitude magnitude in degrees=52 produce spherical parallel arc distance=147.75875407815798.
Where this model stops being reliable
Geodetic versus geocentric latitude, ellipsoidal radius of curvature, datum, height, and antimeridian handling affect real geodetic work.
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 Parallel Arc Distance works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Geodetic Parallel Arc Distance uses c=a cos(b). 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
- Angles in degrees and radians
Interpreting the angle convention is essential for understanding the inputs and output of Geodetic Parallel Arc Distance.
Review this foundation about 5 min
Optional enrichment
- Functions and their graphs
Function graphs show how the Geodetic Parallel Arc Distance relationship changes across a full angle or period.
Review this foundation about 6 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 equatorial arc distance for the same longitude interval, geocentric latitude magnitude in degrees.
- Evaluate the principal relationship: c=a cos(b).
- Return spherical parallel arc distance and check the domain conditions described above.
Python
from math import *
def geodetic_parallel_arc_distance_calculator(a, b) -> float:
return (a * cos(((b * pi) / 180.0)))
assert abs(geodetic_parallel_arc_distance_calculator(240, 52) - 147.75875407815798) < 1e-6 * max(1.0, abs(147.75875407815798))
C
#include <assert.h>
#include <math.h>
double geodetic_parallel_arc_distance_calculator(double a, double b) {
return (a * cos(((b * 3.141592653589793) / 180.0)));
}
int main(void) {
const double expected = 147.75875407815798;
const double actual = geodetic_parallel_arc_distance_calculator(240, 52);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double geodetic_parallel_arc_distance_calculator(double a, double b) {
return (a * std::cos(((b * std::numbers::pi) / 180.0)));
}
int main() {
constexpr double expected = 147.75875407815798;
const double actual = geodetic_parallel_arc_distance_calculator(240, 52);
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_parallel_arc_distance_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern cos
global geodetic_parallel_arc_distance_calculator
section .text
geodetic_parallel_arc_distance_calculator:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x400921fb54442d18
movq xmm0, rax
movsd [rbp-56], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-56]
movsd [rbp-48], xmm0
mov rax, 0x4066800000000000
movq xmm0, rax
movsd [rbp-64], xmm0
movsd xmm0, [rbp-48]
divsd xmm0, [rbp-64]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
call cos wrt ..plt
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = geodetic_parallel_arc_distance_calculator(a, b)
result = (a * cos(((b * pi) / 180.0)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * Cos[((b * Pi) / 180.0)]);
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 Parallel Arc Distance Calculator. MW SysArc Tools. https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator
MLA 9
MW SysArc. “Geodetic Parallel Arc Distance Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Geodetic Parallel Arc Distance Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator.
Harvard
MW SysArc (2026) ‘Geodetic Parallel Arc Distance Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_geodetic_parallel_arc_distance_calculator_2026,
author = {{MW SysArc}},
title = {Geodetic Parallel Arc Distance Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Geodetic Parallel Arc Distance Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/trigonometry/geodetic-parallel-arc-distance-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Geodetic Parallel Arc Distance do?
Calculate spherical parallel arc distance from equatorial arc distance for the same longitude interval and geocentric latitude magnitude in degrees.
How does the Geodetic Parallel Arc Distance work?
The calculator applies c=a cos(b). On a sphere, an east-west arc along a parallel is the corresponding equatorial arc multiplied by cosine of latitude. This page evaluates the relationship directly.
What can I learn from the Geodetic Parallel Arc Distance?
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 .