Mathematics · Geometry
Longitude Parallel Distance Calculator
Calculate parallel arc distance from equatorial longitude-arc distance and latitude 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 longitude-arc distance=111.32 and latitude in degrees=45.
- parallel arc distance=78.71512688168647.
Understand Longitude Parallel Distance
One idea, three depths
Choose how deeply to explain Longitude Parallel Distance
Longitude Parallel Distance: Calculate parallel arc distance from equatorial longitude-arc distance and latitude in degrees.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Longitude Parallel Distance to answer this question: calculate parallel arc distance from equatorial longitude-arc distance and latitude in degrees? Enter equatorial longitude-arc distance and latitude in degrees; the calculator shows parallel arc distance. For example: equatorial longitude-arc distance=111.32 and latitude in degrees=45 produce parallel arc distance=78.71512688168647. The answer tells you parallel arc distance.
Age 15Explain it to a 15-year-oldConnect it to the formula
On a spherical model, one longitude interval at latitude contracts from its equatorial distance by cosine of latitude. This page evaluates the relationship directly. The rule is c=a cos(b). Its input values are equatorial longitude-arc distance, latitude in degrees, and the main result is parallel arc distance. For example: equatorial longitude-arc distance=111.32 and latitude in degrees=45 produce parallel arc distance=78.71512688168647.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated longitude parallel distance relation over the valid real-number domain stated below. The implemented relation is c=a cos(b), evaluated from equatorial longitude-arc distance, latitude in degrees to produce parallel arc distance. On a spherical model, one longitude interval at latitude contracts from its equatorial distance by cosine of latitude. This page evaluates the relationship directly. Ellipsoidal Earth models and high-precision surveying require latitude-dependent radii.
Inputs and valid domain
- equatorial longitude-arc distance must be a finite real number.
- latitude in degrees must be a finite real number.
Important boundary: Ellipsoidal Earth models and high-precision surveying require latitude-dependent radii.
The formula
c=a cos(b)
How the calculator works through it
It substitutes equatorial longitude-arc distance, latitude in degrees into the formula and exposes every numerical step above. The main output is parallel arc distance.
Read the result correctly
The parallel arc distance is the direct answer to “calculate parallel arc distance from equatorial longitude-arc distance and latitude 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 longitude-arc distance=111.32 and latitude in degrees=45 produce parallel arc distance=78.71512688168647.
Where this model stops being reliable
Ellipsoidal Earth models and high-precision surveying require latitude-dependent radii.
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 Longitude Parallel Distance works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Longitude Parallel 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
- Ratios between measured quantities
Ratios help you check the scale, units and proportional meaning of Longitude Parallel Distance.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Longitude Parallel Distance 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 equatorial longitude-arc distance, latitude in degrees.
- Evaluate the principal relationship: c=a cos(b).
- Return parallel arc distance and check the domain conditions described above.
Python
from math import *
def longitude_parallel_distance_calculator(a, b) -> float:
return (a * cos(((b * pi) / 180.0)))
assert abs(longitude_parallel_distance_calculator(111.32, 45) - 78.71512688168647) < 1e-6 * max(1.0, abs(78.71512688168647))
C
#include <assert.h>
#include <math.h>
double longitude_parallel_distance_calculator(double a, double b) {
return (a * cos(((b * 3.141592653589793) / 180.0)));
}
int main(void) {
const double expected = 78.71512688168647;
const double actual = longitude_parallel_distance_calculator(111.32, 45);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double longitude_parallel_distance_calculator(double a, double b) {
return (a * std::cos(((b * std::numbers::pi) / 180.0)));
}
int main() {
constexpr double expected = 78.71512688168647;
const double actual = longitude_parallel_distance_calculator(111.32, 45);
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 longitude_parallel_distance_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern cos
global longitude_parallel_distance_calculator
section .text
longitude_parallel_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 = longitude_parallel_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). Longitude Parallel Distance Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator
MLA 9
MW SysArc. “Longitude Parallel Distance Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Longitude Parallel Distance Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator.
Harvard
MW SysArc (2026) ‘Longitude Parallel Distance Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_longitude_parallel_distance_calculator_2026,
author = {{MW SysArc}},
title = {Longitude Parallel Distance Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Longitude Parallel Distance Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/longitude-parallel-distance-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Longitude Parallel Distance do?
Calculate parallel arc distance from equatorial longitude-arc distance and latitude in degrees.
How does the Longitude Parallel Distance work?
The calculator applies c=a cos(b). On a spherical model, one longitude interval at latitude contracts from its equatorial distance by cosine of latitude. This page evaluates the relationship directly.
What can I learn from the Longitude Parallel 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 .