How circle measurements relate to each other
The table below shows how to derive the radius from each of the four possible known values.
| Known value | Radius formula |
|---|---|
| Radius (r) | r = r |
| Diameter (d) | r = d / 2 |
| Circumference (C) | r = C / (2π) |
| Area (A) | r = √(A / π) |
- π (pi) is an irrational number, approximately 3.14159265; results shown use a high-precision floating-point value of π, not a rounded approximation like 3.14 or 22/7.
- Diameter is always exactly twice the radius (d = 2r); confusing the two is one of the most common circle-calculation errors.
What defines a circle's measurements?
A circle is fully defined by a single measurement — its radius, the distance from its center to any point on its edge. Every other measurement (diameter, circumference and area) can be derived from the radius alone using fixed geometric relationships involving π (pi), the ratio of a circle's circumference to its diameter, approximately 3.14159.
Because all four quantities are mathematically linked, providing any one of them is enough to derive the other three — this calculator accepts any of the four as the starting point.
How to use this circle calculator
- Select which value you know: radius, diameter, circumference or area.
- Enter that value in the input field.
- The calculator derives the radius internally, then computes all four measurements from it.
- Read the radius, diameter, circumference and area, which update instantly as you change the input.
The formulas behind circle measurements
All circle formulas are derived from the radius; when a different value is entered, the calculator first solves for the equivalent radius before computing the rest.
Common mistakes
- Entering the diameter into a field expecting the radius (or vice versa), which doubles or halves every derived result.
- Using a rounded value of π (such as 3.14) for hand calculations and then comparing against this calculator's higher-precision result, producing small discrepancies.
- Forgetting to take the square root when deriving radius from area — r = √(A/π), not A/π.
- Mixing units, such as entering circumference in centimeters but expecting area in square meters.
Pertanyaan yang sering diajukan
How do you find the circumference of a circle from its radius?
Circumference equals 2 × π × radius. A circle with radius 5 has a circumference of 2 × π × 5 ≈ 31.4159 units.
How do you find the area of a circle from its radius?
Area equals π × radius². A circle with radius 5 has an area of π × 25 ≈ 78.5398 square units.
How do you find the radius from the area of a circle?
Rearrange the area formula and take the square root: r = √(A / π). A circle with area 78.5398 has a radius of √(78.5398 / π) = √25 = 5.
What is the difference between radius and diameter?
The radius is the distance from a circle's center to its edge; the diameter is the distance across the circle through its center, and is always exactly twice the radius (d = 2r).
How do you find the diameter from the circumference?
Since circumference equals π × diameter, diameter equals circumference divided by π. A circle with a circumference of 31.4159 has a diameter of 31.4159 / π ≈ 10.
What value of π does this calculator use?
The calculator uses the full double-precision floating-point value of π built into JavaScript (approximately 3.14159265358979), not a rounded classroom approximation, so results are accurate to six decimal places.
Referensi
- NIST Guide to the SI — circular measurement conventions.
- Weisstein, Eric W. "Circle" and "Pi." MathWorld — A Wolfram Web Resource.