Arc Length Calculator

This calculator solves the arc of a circle from any two of its three measurements. Give it a radius and a central angle in degrees or radians and it returns the arc length, the chord across the ends, the sector area and the segment area; give it an arc length instead and it works back to the angle or to the radius. A fourth mode works backwards from a chord and the height of the arc above it to the radius, angle and arc length. Every answer comes from s = r x theta, so the arithmetic is exact rather than approximated. It is scoped to circular arcs on purpose: the length of a general curve is an integral of sqrt(1 + f'(x)^2), which needs symbolic calculus this page does not have.

Calculator Type
Angle Units

The usual direction: a radius and the angle at the centre give the arc, the chord and the areas.

Any unit you like. The lengths come back in that unit and the areas in its square.
The angle at the centre of the circle, between the two radii that meet the ends of the arc. At most one full turn: 360 degrees or 6.283185 radians.
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You measured the arc and you know the radius. This returns the angle it subtends, in both units.

Any unit you like. The angle it gives back is the same whichever you use, as long as the radius below is in the same one.
Use the same unit as the arc length.
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Angle Units

The arc is known and so is the angle it turns through, which fixes the circle it came from.

The angle at the centre of the circle, between the two radii that meet the ends of the arc. At most one full turn: 360 degrees or 6.283185 radians.
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You can measure the straight span and how high the arc rises above its middle, as on an arched window, a curved wall or a bent rail. This finds the circle and everything that follows from it.

The straight line between the two ends of the arc. Any unit you like.
From the middle of the chord straight up to the arc. Use the same unit as the chord.
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