Circle Calculator
Solve a circle's radius, diameter, circumference and area from any one value, plus arc and sector.
What do you know about the circle?
- Radius (r)
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- Diameter (d)
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- Circumference (C)
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- Area (A)
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Arc, chord and sector
- Arc length
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- Chord length
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- Sector area
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- Angle in radians
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Formulas used
- d = 2r
- C = 2πr = πd
- A = πr²
- arc = 2πr × (θ / 360)
- chord = 2r × sin(θ / 2)
- sector A = πr² × (θ / 360)
How it works
Pick whichever measurement you already have — radius, diameter, circumference or area — type it in, and the other three are solved instantly. The tool works backwards through the standard circle formulas: the radius comes from d ÷ 2, C ÷ 2π or √(A ÷ π), and everything else follows from C = 2πr and A = πr². Choose a unit and the results are labelled for you, with squared units on the areas so you can paste them straight into homework or a spec sheet.
The second block covers a slice of the circle: enter a central angle in degrees and you get the arc length, the straight chord across it, the sector area and the angle in radians. Set the decimal places to 2 for a quick answer or 10 when you need the full precision of JavaScript's Math.PI. Everything is calculated in your browser — nothing is uploaded, there are no ads and no sign-up.
Frequently asked questions
How do you find the radius from the area of a circle?
Divide the area by π and take the square root: r = √(A ÷ π). An area of 100 gives a radius of 5.6419, a diameter of 11.2838 and a circumference of 35.4491. Set "Known value" to Area, type your number and the tool does exactly that calculation live.
What is the difference between circumference and diameter?
The diameter is the straight line across the circle through its centre (d = 2r); the circumference is the distance all the way around the edge (C = πd = 2πr). The circumference is always about 3.14159 times the diameter, so a circle 10 cm across has a circumference of 31.4159 cm.
How do I calculate arc length and sector area from a central angle?
An angle θ covers θ/360 of the circle, so arc = 2πr × (θ ÷ 360) and sector area = πr² × (θ ÷ 360); the chord across it is 2r × sin(θ ÷ 2). Enter the angle in degrees in the second block and all three are shown, along with the angle in radians.