Mathematics · Geometry
Circle Chord Sagitta half-chord length Solver
Rearrange the circle chord sagitta relationship and solve for half-chord length.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=√(2ac−c²) with sagitta=2 and circle radius=10.
- half-chord length=6.
- Substitution into c=a−√(a²−b²) reconstructs 2.
Understand Circle Chord Sagitta: solve half-chord length
One idea, three depths
Choose how deeply to explain Circle Chord Sagitta: solve half-chord length
Circle Chord Sagitta: solve half-chord length: Rearrange the circle chord sagitta relationship and solve for half-chord length.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Circle Chord Sagitta: solve half-chord length to answer this question: rearrange the circle chord sagitta relationship and solve for half-chord length? Enter sagitta and circle radius; the calculator shows half-chord length. For example: circle radius=10 and half-chord length=6 produce sagitta=2. The answer tells you half-chord length.
Age 15Explain it to a 15-year-oldConnect it to the formula
Sagitta is the radial height between a chord midpoint and its circular arc. This page isolates half-chord length and verifies it in the original relationship. The rule is b=√(2ac−c²). Its input values are sagitta, circle radius, and the main result is half-chord length. For example: circle radius=10 and half-chord length=6 produce sagitta=2.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated circle chord sagitta: solve half-chord length relation over the valid real-number domain stated below. The implemented relation is b=√(2ac−c²), evaluated from sagitta, circle radius to produce half-chord length. Sagitta is the radial height between a chord midpoint and its circular arc. This page isolates half-chord length and verifies it in the original relationship. Half-chord length cannot exceed the radius, and this uses the minor-segment sagitta.
Inputs and valid domain
- sagitta must be a finite real number.
- circle radius must be a finite real number.
Important boundary: Half-chord length cannot exceed the radius, and this uses the minor-segment sagitta.
The formula
b=√(2ac−c²)
How the calculator works through it
It substitutes sagitta, circle radius into the formula and exposes every numerical step above. The main output is half-chord length, accompanied by Reconstructed sagitta.
Read the result correctly
The half-chord length is the direct answer to “rearrange the circle chord sagitta relationship and solve for half-chord length.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
circle radius=10 and half-chord length=6 produce sagitta=2.
Where this model stops being reliable
Half-chord length cannot exceed the radius, and this uses the minor-segment sagitta.
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 Circle Chord Sagitta: solve half-chord length works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Circle Chord Sagitta: solve half-chord length uses b=√(2ac−c²). 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 Circle Chord Sagitta: solve half-chord length.
Review this foundation about 4 min
Optional enrichment
- Angles and geometric relationships
Angle language provides useful geometric context for extending Circle Chord Sagitta: solve half-chord length 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 sagitta, circle radius.
- Evaluate the principal relationship: b=√(2ac−c²).
- Return half-chord length and check the domain conditions described above.
Python
from math import *
def circle_chord_sagitta_solve_b(c, a) -> float:
return sqrt(((2.0 * (a * c)) - (c * c)))
assert abs(circle_chord_sagitta_solve_b(2, 10) - 6) < 1e-6 * max(1.0, abs(6))
C
#include <assert.h>
#include <math.h>
double circle_chord_sagitta_solve_b(double c, double a) {
return sqrt(((2.0 * (a * c)) - (c * c)));
}
int main(void) {
const double expected = 6;
const double actual = circle_chord_sagitta_solve_b(2, 10);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double circle_chord_sagitta_solve_b(double c, double a) {
return std::sqrt(((2.0 * (a * c)) - (c * c)));
}
int main() {
constexpr double expected = 6;
const double actual = circle_chord_sagitta_solve_b(2, 10);
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 circle_chord_sagitta_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global circle_chord_sagitta_solve_b
section .text
circle_chord_sagitta_solve_b:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4000000000000000
movq xmm0, rax
movsd [rbp-48], xmm0
movsd xmm0, [rbp-16]
mulsd xmm0, [rbp-8]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-48]
mulsd xmm0, [rbp-56]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-8]
movsd [rbp-64], xmm0
movsd xmm0, [rbp-40]
subsd xmm0, [rbp-64]
movsd [rbp-32], xmm0
sqrtsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = circle_chord_sagitta_solve_b(c, a)
result = sqrt(((2.0 * (a * c)) - (c * c)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := Sqrt[((2.0 * (a * c)) - (c * c))];
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). Circle Chord Sagitta half-chord length Solver. MW SysArc Tools. https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver
MLA 9
MW SysArc. “Circle Chord Sagitta half-chord length Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Circle Chord Sagitta half-chord length Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver.
Harvard
MW SysArc (2026) ‘Circle Chord Sagitta half-chord length Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_circle_chord_sagitta_solve_b_2026,
author = {{MW SysArc}},
title = {Circle Chord Sagitta half-chord length Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Circle Chord Sagitta half-chord length Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/geometry/circle-chord-sagitta-half-chord-length-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Circle Chord Sagitta: solve half-chord length do?
Rearrange the circle chord sagitta relationship and solve for half-chord length.
How does the Circle Chord Sagitta: solve half-chord length work?
The calculator applies b=√(2ac−c²). Sagitta is the radial height between a chord midpoint and its circular arc. This page isolates half-chord length and verifies it in the original relationship.
What can I learn from the Circle Chord Sagitta: solve half-chord length?
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 .