Circle Calculator

Calculate all circle properties from any single known value: radius, diameter, circumference, or area.

100% Free No Sign-Up Calculated in Your Browser

Known Property

Value

Arc & Sector

Central Angle (°)

Area

Enter a value to calculate all properties

Radius

Diameter

Circumference

Arc Length

Sector Area

Chord Length

Radius	Diameter	Circumference	Area

Enter any one known circle property — radius, diameter, circumference, or area — to instantly derive all the others, plus arc length, sector area, and chord length for any chosen angle.

How It Works

How Circle Calculator Works

Whichever property you enter, the calculator first solves for the radius (for example, from area A it computes r=√(A/π); from circumference C, r=C/(2π)), then derives every other property from that radius using the standard circle formulas: area=πr², circumference=2πr, and diameter=2r.

For a chosen central angle θ (in degrees), arc length = circumference × (θ/360) and sector area = full circle area × (θ/360) — both scale in direct proportion to the fraction of the full 360° circle that angle represents.

Chord length — the straight line connecting the two endpoints of the arc — uses chord = 2r × sin(θ/2), which comes from splitting the isosceles triangle formed by the two radii and the chord into two equal right triangles, each with half the central angle.

Worked Example

See It In Action

A circle with radius 5: area = π×5² ≈ 78.54 sq units, circumference = 2π×5 ≈ 31.42 units, and diameter = 10. For a 90° sector: arc length = 31.42×(90/360) ≈ 7.85, sector area ≈ 19.63 sq units, and the chord connecting the arc's two endpoints = 2×5×sin(45°) ≈ 7.07.

Real-World Use Cases

Who Uses Circle Calculator and Why

Finding a circle's full set of properties (radius, diameter, circumference, area) starting from whichever single measurement you actually have on hand.
Calculating a pizza slice or pie-chart sector's area from its central angle.
Computing the arc length of a curved track or path segment for a design or engineering problem.
Finding a chord's length for an arch or bridge design given a radius and central angle.

Common Mistakes

Mistakes to Avoid

Entering a diameter value into a field expecting a radius (or the reverse), which throws off every other derived property.
Forgetting that sector area and arc length both scale directly with the fraction of 360° the central angle represents, so a wrong angle unit or value skews both results proportionally.
Assuming chord length equals arc length — the chord is the straight-line distance between the arc's two endpoints, always shorter than the curved arc itself.

Pro Tips

Tips for Best Results

Enter whichever property (radius, diameter, circumference, or area) you actually measured directly, and let the calculator derive the radius and everything else from it.
Double-check the central angle is entered in degrees, since arc length, sector area, and chord length all depend directly on it.

Troubleshooting

Fixing Common Problems

My sector area or arc length looks too small or too large. — Confirm the central angle was entered correctly in degrees — both values scale directly with the fraction of the full 360° circle that angle represents, so a wrong angle throws off the result proportionally.

Glossary

Terms Explained

Chord: The straight-line segment connecting the two endpoints of an arc, always shorter than the arc itself for angles less than 360°.

Central angle: The angle at a circle's center defining an arc or sector, measured in degrees out of a full 360° circle.

FAQ

Frequently Asked Questions

Can I start from area or circumference instead of radius?

Yes — select whichever property you already know (radius, diameter, circumference, or area) from the dropdown, and the calculator solves for the radius from that value first before deriving everything else.

What's the difference between arc length and chord length?

Arc length is the distance measured along the curved edge of the circle between two points, while chord length is the straight-line distance directly connecting those same two points — the chord is always shorter than the arc it subtends (except for a full 360° "arc," where they're unrelated concepts).

How is sector area related to the full circle's area?

A sector's area is simply the full circle's area (πr²) scaled down by whatever fraction of 360° its central angle covers — a 90° sector, for instance, covers exactly a quarter of the full circle's area.

Why does the chord formula use sin(θ/2) instead of sin(θ)?

Drawing a line from the circle's center perpendicular to the chord bisects both the chord and the central angle, creating two identical right triangles — each uses half the original angle, which is why the formula involves θ/2 rather than the full θ.