Arc Length Calculator

Calculate the arc length of linear, quadratic, and circular curves between two points using numerical integration.

Curve Type

Coefficient a

Coefficient b

x Start

x End

Tab to move between fields

Arc Length

4.64678

Chord Length4.47214

Arc/Chord Ratio1.0391

How to Use This Calculator

Select the curve type (linear, quadratic, or circular) and enter its defining parameters.
Enter the lower and upper bounds (a and b) along the x-axis over which to measure the arc length.
Arc length L = ∫[a to b] √(1 + (f'(x))²) dx; the calculator evaluates this integral numerically.
For a circle segment, arc length = r × θ (radius times central angle in radians), which is computed analytically.
The curve chart shows the segment of the function between the two bounds so you can visually verify the range.
Arc length is always ≥ the straight-line distance between the endpoints (chord length).

How the result changes with x End

Identify Input Parameters
4 parameters
Curve Type = 2, Coefficient a = 1, Coefficient b = 0, x Start = 0 = 5 input(s) provided
Calculate Arc Length
Arc Length
4.64678 = 4.64678
Calculate Chord Length
Chord Length
4.47214 = 4.47214
Calculate Arc/Chord Ratio
Arc/Chord Ratio
1.0391 = 1.0391

Engine last updated August 5, 2026. Checked against 3 independently-derived tests — how we verify calculators.

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