Arc length calculator
Calculate the length of a curve y = f(x) between two points using the arc length formula with integration.
f(x) =
From x =
to x =
Arc length formula
L = ∫ₐᵇ √(1 + [f'(x)]²) dx
First find the derivative f'(x), square it, add 1, take the square root, then integrate from a to b.
Example: y = x² from 0 to 1
f'(x) = 2x. L = ∫₀¹ √(1 + 4x²) dx ≈ 1.4789.
When the integral is hard
Most arc length integrals don't have clean closed-form solutions. This calculator uses both symbolic and numerical methods to give you the most accurate result possible.
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