Circle Calculator
Find area, circumference, diameter, and radius of any circle.
Results
What is a Circle Calculator?
A circle calculator computes the four key measurements of any circle — area, circumference, diameter, and radius — from a single known value. Because every property of a circle is linked through the constant π (pi, approximately 3.14159), knowing just one measurement is enough to derive all the others.
This tool comes in handy for homework, woodworking, sewing, landscaping, and any project that involves round shapes: figuring out how much fabric covers a circular table, how far you walk around a round track, or whether a 14-inch pizza is really much bigger than a 12-inch one. Enter the radius or diameter, and the calculator shows the rest instantly, rounded to four decimal places.
The Circle Formulas
All four properties follow from three short equations, which the calculator applies directly:
Diameter: d = 2r
Circumference: C = 2πr (equivalently, C = πd)
Area: A = πr²
- Radius (r) — the distance from the center of the circle to any point on its edge. This is the value every formula is built on.
- Diameter (d) — the distance straight across the circle through its center, always exactly twice the radius. If you enter a diameter, the calculator halves it first and then works from the radius.
- π (pi) — the ratio of a circle's circumference to its diameter, roughly 3.14159. The calculator uses π to full floating-point precision rather than a rounded approximation.
Worked Example: A 12-Inch Pizza
Say you order a 12-inch pizza and want to know how much pizza you are actually getting. A pizza's stated size is its diameter, so select Diameter mode and enter 12:
- Radius: r = d ÷ 2 = 12 ÷ 2 = 6 inches.
- Area: A = π × 6² = π × 36 = 113.0973355... ≈ 113.0973 square inches of pizza.
- Circumference (the length of the crust edge): C = 2π × 6 = 12π = 37.6991118... ≈ 37.6991 inches.
Now compare a 14-inch pizza, whose radius is 7 inches. Its area is π × 7² = 49π = 153.9380 square inches, and 153.9380 ÷ 113.0973 ≈ 1.361 — about 36% more pizza from a diameter that is only 2 inches wider. Area grows with the square of the radius, so a small bump in diameter buys a lot more food.
Quick Reference: Common Circle Measurements
Values below are rounded to four decimal places, matching the calculator's display. Any unit works — inches, centimeters, meters — as long as you keep it consistent; circumference comes out in that unit and area in that unit squared.
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 3 | 6 | 18.8496 | 28.2743 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
A curiosity visible in the table: at radius 2, circumference and area share the same numeric value (12.5664), because 2πr equals πr² exactly when r = 2. Above that point, area pulls ahead quickly — by radius 10 it is numerically five times the circumference.
How to Use
- Choose the Radius or Diameter input mode, depending on which measurement you know.
- Enter the value in the input field — the label updates to match the mode you picked.
- Click Calculate to see the area, circumference, diameter, and radius, along with the formulas used.
- Click Reset to clear the input and results and start over.
Frequently Asked Questions
What if I only know the circumference?
Work backwards: radius = C ÷ (2π) and diameter = C ÷ π. For example, if a round rug measures 44 inches around, its radius is 44 ÷ (2π) ≈ 7.0028 inches and its diameter is 44 ÷ π ≈ 14.0056 inches. Enter 7.0028 in Radius mode to get the full set of measurements.
Can I use this for spheres?
No, this tool is for flat, two-dimensional circles only. Use our Volume Calculator for spheres, cylinders, and other 3D shapes.
Are the results exact?
The calculator uses π to full floating-point precision (3.141592653589793) and rounds results to four decimal places for display. For a radius of 1, the exact area is π itself, which appears as 3.1416.
What is the difference between radius and diameter?
The radius runs from the center of the circle to its edge; the diameter runs from edge to edge through the center and is always exactly twice the radius (d = 2r). Measuring across the widest part of a round object gives you the diameter.
Does doubling the radius double the area?
No — it quadruples it. A circle with radius 3 has an area of 28.2743 square units, while radius 6 gives 113.0973, exactly four times as much, because area depends on r². The circumference, by contrast, does exactly double, since it scales with r directly.
How do I find the area if I only know the diameter?
Halve the diameter to get the radius, then apply A = πr². For a 12-inch circle: r = 6, so A = π × 36 ≈ 113.0973 square inches. This calculator does the halving for you when you use Diameter mode.
Is this tool free?
Yes, BestCalc calculators are completely free and run entirely in your browser.