Calculate arc length, sector area, chord length, and other circle measurements instantly. Enter any two values to solve the remaining geometry automatically.
Enter values to see calculation results
This arc length calculator with sector area lets you start with the two measurements you already know and solve the rest automatically. That works well for classroom geometry, design layouts, curved construction details, and any job where the circle data comes from different sources.
Use radius and angle, arc length and angle, chord length and radius, or another compatible input pair.
Match the problem exactly by choosing degrees for angle values like 45° or radians for values like π/4.
LiteCalc returns arc length, sector area, chord length, radius, diameter, circumference, and angle conversions together.
Keep length units consistent and confirm whether the problem uses a minor arc or major arc before trusting the final answer.
The arc length formula depends on whether your angle is measured in degrees or radians. For degrees: Arc Length = (θ/360°) × 2πr. For radians: Arc Length = θ × r, where θ is the central angle and r is the radius.
Arc length calculations are essential in engineering, architecture, manufacturing, and design. They're used for creating curved roads, designing circular structures, calculating material requirements for curved surfaces, and solving navigation problems.
Degrees divide a circle into 360 equal parts, while radians use the radius as the unit of measurement. One complete circle equals 360° or 2π radians. Radians are often preferred in advanced mathematics and physics calculations.
The distance along the curved line that forms part of the circumference of a circle.
The angle formed by two radii that meet at the center of the circle.
The region of a circle enclosed by two radii and the arc between them, like a slice of pie.
The distance from the center of the circle to any point on its circumference.
The complete distance around the circle, calculated as 2πr.
When working with arc length problems, always check your angle units. Converting between degrees and radians is a common source of calculation errors. Remember: 180° = π radians.
The calculator reports several circle measurements together because they all describe the same geometry from different angles. Seeing them side by side helps you check whether the answer is reasonable before you use it in class, design work, or estimating.
Arc length is the curved distance along the circle. Use it when you need the actual curved edge for trim, track curves, irrigation arcs, pipe bends, or any rounded path.
Sector area is the wedge-shaped region between two radii and the arc. It matters when you estimate mulch, flooring, paint, or other coverage inside a curved slice of a circle.
Chord length is the straight-line distance between the arc endpoints. Comparing chord length with arc length helps you see how deep or shallow the curve really is.
Radius tells you the circle size. Diameter is twice the radius. Circumference is the full distance around the circle. Together, they help you judge whether your arc is a small slice, a half circle, or almost a full revolution.
The percent of circle result is especially useful for quick checks. If your arc is about 25% of the circumference, the angle should be near 90 degrees.
The calculator shows both angle formats because geometry problems often switch between them. Anchor conversions worth remembering are 45° = π/4, 90° = π/2, 180° = π, and 360° = 2π.
Arc length is a fraction of the full circumference. Sector area is the matching fraction of the full circle area. That shared logic is why one set of circle formulas can solve several measurements.
In these formulas, r is the radius and θ is the central angle in radians. If the angle starts in degrees, convert it by multiplying by π/180 before using the radian formulas.
That direct relationship is why this page works as an arc length calculator in degrees and radians, a sector area solver, and a chord helper all at the same time.
Suppose a quarter-circle garden bed has a radius of 12 feet and a central angle of 90°.
One setup gives you the curved border length, the wedge area, and the straight span between the end points.
Arc length appears in more real-world situations than many people expect. These examples use realistic numbers so you can connect the formulas to practical decisions.
A quarter-circle patio with an 8 ft radius has an arc length of 12.57 ft and a sector area of 50.27 sq ft. That helps estimate edging and surface coverage.
A sprinkler with a 12 ft radius and a 120° sweep covers an arc length of 25.13 ft and a sector area of 150.80 sq ft.
For a 60° window arch with an 18 in radius, the arc length is 18.85 in and the chord length is 18 in.
A 180° bend with a 15 m radius creates a curved path of 47.12 m, which matters over repeated laps.
Two points on a circle create two possible arcs. Choosing the wrong one changes the answer, so it is worth checking before you use the result in a drawing, estimate, or worksheet.
The minor arc is the shorter path between two points on the circle. Its central angle is less than 180°. Most basic geometry questions default to the minor arc unless they say otherwise.
The major arc is the longer path around the circle. Its central angle is greater than 180°. If the minor arc is 120°, the major arc is 240°, which changes every other result.
Keep going with more LiteCalc tools for circle, area, conversion, and geometry work.
Find circumference, diameter, radius, and area from a single known circle measurement.
Calculate area for circles, rectangles, triangles, trapezoids, and more from one page.
Convert between inches, feet, meters, and other units before you solve a geometry problem.
Move from 2D sector geometry to 3D shape calculations when your project involves cones, cylinders, or spheres.
Estimate floors, patios, and outdoor spaces after you work out the sector dimensions of a curved area.
Simplify values when your angle uses fractions of pi or exact classroom-style expressions.
Answers to the most common arc length, sector area, and chord length questions.
Arc length is the distance measured along the curved part of a circle between two points. It is a portion of the full circumference and depends on the radius and the central angle.
If the angle is in radians, multiply the radius by the central angle: s = r × θ. If the angle is in degrees, first convert it to radians or use s = (θ/360) × 2πr.
Yes. You can either convert degrees to radians first or use the degree-based formula s = (θ/360) × 2πr. This calculator handles both angle units automatically.
Arc length is the curved distance along the circle, while chord length is the straight-line distance between the arc endpoints. For the same two points, the chord is shorter than the minor arc.
If you know the radius and arc length, use A = 1/2 × r × s. If you know the radius and central angle in radians, use A = 1/2 × r² × θ. Both relationships are shown on this page.
Yes. Enter any two compatible values, such as arc length and central angle or chord length and radius, and the calculator solves the missing circle measurements automatically.
An angle greater than 360 degrees represents more than one full turn. The arc length keeps increasing because it includes full revolutions plus the extra arc.
Use the major arc when the path you care about is the longer way around the circle and the central angle is greater than 180 degrees. Use the minor arc when you want the shorter path between two points.
The formulas assume all length measurements use the same unit, such as inches, feet, centimeters, or meters. Matching units keeps the outputs consistent and prevents scaling errors.