Calculated using standard mathematical and industry formulas.
Free online Circle Calculator calculator for academic, engineering, and statistical math.
How to use this calculator?
Select which property you already know: radius, diameter, circumference, or area.
Enter its value — the other three properties compute instantly.
Optionally enter a central angle (in degrees) to get the arc length and sector area for that slice.
Formula & calculation method
Circle properties from radius
d = 2r · C = 2πr · A = πr² · Arc length = (θ/360) × 2πr · Sector area = (θ/360) × πr²
r = radius, d = diameter, C = circumference, A = area, θ = central angle in degrees.
Step-by-step calculation example
Circle with r = 5: d = 10, C = 2π × 5 ≈ 31.42, A = π × 25 ≈ 78.54. 60° sector: arc ≈ 5.24, sector area ≈ 13.09.
Key insights to remember
π ≈ 3.14159 is the ratio C / d for every circle regardless of size.
Doubling the radius quadruples the area (A = πr²), but only doubles the circumference.
A sector is a 'pizza slice'. Its area is (θ/360) × πr² and its arc length is (θ/360) × 2πr.
The circle is the unique shape that maximises area for a given perimeter.
How to interpret your results?
Circumference vs diameter
Their ratio is always π ≈ 3.14159. Knowing one uniquely determines the other.
Sector vs segment
A sector is the pie-slice bounded by two radii and an arc. A segment is the region between a chord and an arc — computed by subtracting the triangle from the sector.
Frequently asked questions
How does the Circle Calculator calculator work?
It uses standard algebraic, geometric, or statistical theorems to return exact values.
How accurate are the results?
All calculations use double-precision floating-point arithmetic for exact accuracy.
Can I copy the step-by-step work?
Yes, step-by-step solutions are formatted clearly for homework or documentation.
How are undefined operations handled?
The calculator flags mathematical errors such as division by zero or negative square roots.
Is this tool suitable for students and engineers?
Yes, it is designed for students, teachers, engineers, and scientists.
Does it support negative numbers and decimals?
Yes, all real numbers (positive, negative, fractions, and decimals) are supported.
Related calculators
Area Calculator — Calculate the area and perimeter of rectangles, squares, circles, triangles, trapezoids, ellipses and parallelograms.
Surface Area Calculator — Calculate total, lateral and base surface areas for spheres, cylinders, cones, cubes, rectangular prisms and tori.
Triangle Calculator — Solve any triangle from sides or angles using SSS, SAS, ASA, or AAS — area, perimeter, angles and heights.