DIY Cost Tools
Arc Length Calculator
MATH & GEOMETRY CALCULATOR
Calculate circular arc length, chord length, and angle in radians.
Use the same length unit throughout. All fields are required. Assumes constant radius and a central angle from zero to 360 degrees. Angles above 180 describe the major arc.
How to use this calculator
Enter your dimensions and select Calculate. Length results use your input unit, areas use its square, and volumes use its cube. Retain measurement precision until the final answer.
Formula and explanation
Arc = rθπ/180; chord = 2r sin(θπ/360); radians = θπ/180
The arc follows the curve; the chord connects its endpoints in a straight line.
Worked example
For Radius (units) = 10, Central angle (degrees) = 90, results are Arc length (units): 15.707963; Chord length (units): 14.142136; Angle (radians): 1.5707963.
Important limitations
Assumes constant radius and a central angle from zero to 360 degrees. Angles above 180 describe the major arc.
Ideal geometry does not account for manufacturing tolerances or measurement uncertainty. This is a calculation aid, not a structural design or building-code approval. Absolute inputs must not exceed one trillion.
Frequently asked questions
Why is the chord shorter?
It follows a straight path between endpoints.
What happens at 360 degrees?
The arc equals the circumference and the endpoints meet, giving a zero chord.
Can I mix inches and centimeters?
Convert all lengths to one unit first. Mixed units produce incorrect results.
Why did my result disappear?
Blank, invalid, or out-of-range inputs clear the previous result and display an instruction.
Review notes
Reviewed October 1, 2026. Default results were checked against the displayed formulas. Script tests covered blank, negative, nonfinite, and excessive inputs. Results run locally in your browser.