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Circle Calculator

Enter any one of radius, diameter, circumference or area to get the other three.

A circle has four linked quantities — radius, diameter, circumference and area — and knowing any one of them gives you the other three. Enter the value you have, say which one it is, and all four come back together with a formula reference table. Handy for checking homework, sizing a round table, or working out how much sheet material a circular cut needs.

The formulas are C = 2πr, A = πr² and d = 2r. This tool computes with the full double-precision value of π and rounds only for display: if a textbook or a marking scheme calls for 3.14 or 3.14159, round the answer to that instead — the underlying value never changes. When cutting material, add a percent or two of slack before rounding, since real-world waste is always positive.

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How to use

  1. Choose which quantity you already know (radius, diameter, circumference or area).
  2. Enter its value; the other three update immediately.
  3. Read all four results and the formula reference table.
  4. Round as your context requires — 3.14 for coursework, extra slack before cutting material.

How it works

How the four quantities convert into each other

A circle has only three basic relations: diameter d = 2r, circumference C = 2πr and area S = πr². Knowing any one of the four quantities determines the other three. For radius 5: diameter 10, circumference 31.4159, area 78.5398. When you enter the diameter, circumference or area, the tool first recovers the radius and then derives everything else.

How many digits of π matter

The choice of π affects the digits shown. Internally this tool uses the double-precision π = 3.141592653589793 (about 16 significant digits) and compresses the display to 6 significant digits, so 2π × 5 shows as 31.4159. School problems often use 3.14, which gives 31.4 — a last-digit difference caused by a different precision convention, not a calculation error.

Solving backwards from circumference or area

When solving backwards, recover the radius first: from circumference use r = C ÷ 2π; from area use r = √(S ÷ π). Note that area involves a square, so precision drops slightly after the square root — working back from an area of 78.5398 still gives radius 5, but if the input area was itself rounded, the decimal digits of the radius will drift. That comes from imprecise input, not the method.

Calculation basis: d = 2r, C = 2πr and S = πr², with π taken as the double-precision value 3.141592653589793 and results shown to 6 significant digits. Reverse formulas are r = C/(2π) and r = √(S/π).

Code example

JavaScript Give one, get three 

const PI = Math.PI;

function circle({ r, d, c, s }) {
  if (r == null && d != null) r = d / 2;
  if (r == null && c != null) r = c / (2 * PI);
  if (r == null && s != null) r = Math.sqrt(s / PI);
  return { r, d: 2 * r, c: 2 * PI * r, s: PI * r * r };
}

circle({ c: 31.4159 });   // r ≈ 5, s ≈ 78.54

Python The same idea with math.pi 

import math

def circle(r=None, d=None, c=None, s=None):
    if r is None and d is not None: r = d / 2
    if r is None and c is not None: r = c / (2 * math.pi)
    if r is None and s is not None: r = math.sqrt(s / math.pi)
    return {"r": r, "d": 2 * r,
            "c": 2 * math.pi * r, "s": math.pi * r ** 2}

circle(s=78.5398)   # r ≈ 5.0

FAQ

Why is the area of a circle πr²?

Slice the circle into many thin sectors and interleave them into an approximate rectangle: the base is about half the circumference (πr) and the height about the radius r, so the area ≈ πr × r = πr². The finer the slicing, the closer the rectangle — the limit is exactly πr².

Should π be 3.14 or 3.14159?

It depends on the precision you need. School problems usually take 3.14; engineering work needs more digits. This tool computes with double-precision π and shows 6 significant digits; if you hand-compute with 3.14, the last digits will differ slightly (e.g. circumference 31.4159 vs. 31.4). Both are correct at their own precision.

Given the circumference, how do I find the area?

First get the radius r = C ÷ (2π), then substitute into S = πr². Or use the direct conversion S = C² ÷ (4π): a circumference of 31.4159 corresponds to radius 5 and area 78.5398.

Given the area, how do I find the diameter?

Take the square root to get the radius r = √(S ÷ π), then multiply by 2. An area of 78.5398 gives radius 5 and diameter 10. Mind the order: square root first, then double — don't multiply the area by 2 directly.

If the radius doubles, what happens to the circumference and area?

The circumference doubles too (linear, C = 2πr) while the area becomes four times as large (quadratic, S = πr²). This "lengths once, areas twice" intuition carries over to similar figures and to the surface area of spheres.

I keep mixing up diameter and radius — any trick?

The diameter is the chord through the center (d = 2r); the radius runs from the center to the edge. Engineering drawings mark diameter with "⌀". Before substituting into a formula, confirm whether the number you have is a diameter or a radius — mixing them up is the most common mistake.

Are the numbers I enter uploaded anywhere?

No. Everything is computed locally in your browser — nothing is sent to a server and nothing is logged. The calculation history lives only in this browser, can be cleared with one click, and disappears when an incognito window closes.