Circle Length Calculator - Circumference and Arc Length

The circle length calculator returns the full distance around a circle, also called the circumference, from a single radius input, and pairs that result with the arc length for any central angle you specify in degrees or radians. Use it for geometry homework, craft and sewing layouts, fence and trim estimates, mechanical parts, and any drawing where a curved distance around a circle matters.

• • Geometry homework: Solve textbook problems that ask for the circumference of a circle of a given radius, or for the length of a partial arc.
• • Craft, sewing, and trim layouts: Measure the trim length around a circular table, hat, or skirt from a measured radius, and read off the arc length for a partial cut.
• • Fence, border, and pipe runs: Estimate the length of fencing, edging, or pipe that wraps a circular feature on a site plan.
• • Wheels, gears, and pulleys: Cross-check the rolling circumference of a wheel or the belt length around a pulley when you only have the radius.

Every output uses the same linear unit as the radius. If you enter the radius in inches, the circumference, arc length, and diameter all come back in inches, and the area comes back in square inches. That keeps the four results internally consistent so you can pick the one you need without converting.

For partial arcs, the central angle is the lever. A 90 degree angle gives a quarter of the full length, 180 a half, and 360 gives the full circumference back as the arc length. An angle of zero gives a degenerate slice with arc length zero while the circumference and area are still defined by the radius.

When the same radius also needs area and diameter, the Circle Calculator returns those values from the same input.

The calculator applies the standard Euclidean formula for the circumference of a circle and the arc length formula for a circular slice. Both formulas come from the same relationship between a radius and a swept angle, so all four outputs trace back to one radius input.

• r: Radius of the circle, measured from the center to any point on the circle.
• theta: Central angle in radians (the calculator converts from degrees if needed).
• C: Full circle length (circumference) in the same linear unit as r.
• s: Arc length for the given theta, also in the same linear unit as r.

The circumference formula C = 2 * pi * r comes from the definition of pi as the ratio of the circumference of a circle to its diameter. Pi is roughly 3.14159, accurate enough for everyday layouts and most classroom problems.

The arc length formula s = r * theta uses theta in radians. A radian sweeps an arc equal in length to the radius, so when theta equals one radian the arc length equals the radius. A full circle is 2 * pi radians, which is why the arc length returns to the full circumference at 2 * pi radians or 360 degrees.

When you switch the angle unit from degrees to radians, the calculator converts internally, so 90 degrees and pi / 2 radians produce the same arc length. Keep the radius in the same unit across all four results so the comparison is direct.

According to Wolfram MathWorld, the circumference of a circle of radius r is 2*pi*r

For an arc without the full circumference, the Arc Length Calculator returns just the partial length from the same radius and angle.

These four terms describe different ways of measuring a circle. Knowing the difference between circumference and arc length is the most common point of confusion in circle problems.

The ratio between the circumference and the diameter is the same for every circle, and that constant is pi. Changing the radius changes the circumference by the same factor and the area by the square of that factor.

For partial sweeps, the arc length is the same fraction of the full circumference as the central angle is of 360 degrees. A 60 degree arc is one sixth of the full circle, so its length is the circumference divided by six.

If you also need the straight chord, sagitta, or segment area for the same central angle, the Chord Length Calculator gives all of them in one step.

Use the calculator with a clear radius, an angle in the right unit, and a single linear unit so the four results line up.

1. 1 Enter the radius: Type the distance from the center of the circle to any point on the circle. Pick a unit and stay with it for every result.
2. 2 Enter the central angle: Type the angle at the center that the slice sweeps. Use 360 degrees for the full circle, 180 for a half, 90 for a quarter.
3. 3 Choose the angle unit: Match the unit to the value you just entered. The calculator converts the angle to radians internally for the arc length formula.
4. 4 Read the circle length first: Use the circumference as the full distance around the circle. This is the value to use for trim, fence, pipe, or belt runs.
5. 5 Read the arc length for the partial slice: Use the arc length when you need only part of the circle, such as a pie slice, a section of trim, or a section of pipe run.
6. 6 Cross-check with diameter and area: Use the diameter and area rows to verify the radius is sensible. The diameter should be twice the radius, and the area should match a separate area formula.

Suppose you are framing a circular patio with a measured radius of 4 feet and you want the trim length for a 90 degree wedge for a corner. The circumference is 25.13 feet, the arc length for 90 degrees is 6.28 feet (a quarter of the circumference), the diameter is 8 feet, and the area is 50.27 square feet. Use the arc length for the corner trim and the area for ordering base material.

For a flat shape that is not a circle, the Polygon Area Calculator covers regular polygons, irregular polygons, and triangles.

Reading the circumference, arc length, diameter, and area in one step turns a single radius and angle into a complete picture of a circle.

• • Four results from two inputs: Get the full circumference, the arc length, the diameter, and the area in the same step without re-entering numbers.
• • Degrees or radians accepted: Use the angle unit you already have, and the calculator does the radian conversion internally so the arc length comes out the same.
• • Layout and cutting support: Pair the circumference for full trim runs with the arc length for partial cuts so the two stay consistent across one project.
• • Single-formula audit trail: Every result traces back to the same radius, which makes it easy to check against a textbook or a worked example.
• • Decimal-friendly for measured drawings: Decimals and fractions of an inch or centimeter work the same way, so a measured radius and angle give a usable length for the workshop.

Because all four outputs come from the same radius, the calculator also works as a formula checker. Enter a radius and angle from a textbook problem, then read the circumference and arc length to confirm the answer matches your hand calculation.

When the focus is on the area of a circle or another flat shape, the Area Calculator gives a quick result with the same radius.

The formulas are compact, but the choice of input unit and the way the angle and radius are measured can change which result you trust most.

• • The calculator assumes a flat 2D circle. For a sphere, the circle length is the great-circle distance on the surface and uses spherical geometry, not the planar formula.
• • The circumference and arc length are exact for an ideal circle, so treat the result as a working value rather than a certified measurement. Rounded output can differ by a few hundredths from a hand calculation that rounds after every intermediate step.
• • The arc length assumes a single swept angle measured at the center of the circle. For arcs that are not centered on the circle (such as a satellite track), use the chord length and segment area instead.

According to Wolfram MathWorld, the length of a circular arc with radius r and central angle theta in radians is r*theta

According to Wikipedia, the circumference is the perimeter of the circle and equals pi times the diameter

For flooring or paint jobs that use a circular layout, the Square Footage of a Circle Calculator converts the same radius into square feet.