Quick answer
The radius of a circle is half the diameter, r = d ÷ 2 = C ÷ 2π = √(A ÷ π). A diameter of 9 gives a radius of 4.5, a circumference of 28.2743 and an area of 63.6173.
Choose which measurement you know and enter it. The calculator returns the radius and the other circle measurements.
Related tools: Circle Diameter Calculator: Diameter of a circle from radius, circumference or area. Sector Area Calculator: Area and arc length of a circular sector. Arc Length Calculator: Length of a circular arc.
How to use the Radius Calculator
- Choose i know the: Radius, Diameter, Circumference and Area.
- Enter value (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: Radius; Diameter; Circumference; Area | Starts at Radius |
| Value | A number | > 0 |
Formula and method
Formula
d = 2r; C = 2πr; A = πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = Diameter; Value = 9.
| Result | Value |
|---|---|
| Radius | 4.5 |
| Diameter | 9 |
| Circumference | 28.274334 |
| Area | 63.617251 |
Example 2
Inputs: I know the = Area; Value = 78.53981633974483.
| Result | Value |
|---|---|
| Radius | 5 |
| Diameter | 10 |
| Circumference | 31.415927 |
| Area | 78.539816 |
The first line is the headline result (radius). Below it the radius Calculator lists diameter, circumference and area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Three routes to the radius
From the diameter, halve it. From the circumference, divide by 2π: 28.2743 ÷ 6.2832 = 4.5. From the area, divide by π and take the square root: √(63.6173 ÷ 3.1416) = 4.5.
Where it is used
Measure the diameter of a pipe, wheel or circular table and halve it to apply area and volume formulas. The value must be positive, and the radius is in the same unit as the input.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | Radius | Diameter | Circumference |
|---|---|---|---|
| 4.5 | 2.25 | 4.5 | 14.137167 |
| 9 | 4.5 | 9 | 28.274334 |
| 18 | 9 | 18 | 56.548668 |
| 36 | 18 | 36 | 113.097336 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "0" shows "Value must be greater than 0." beside that field and no result.
Choosing between the Radius Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Circle Diameter Calculator](/math/circle-diameter/) | i know the and value | Diameter |
| [Sector Area Calculator](/math/sector-area/) | radius and central angle | Sector area |
| [Arc Length Calculator](/math/arc-length-calculator/) | radius and central angle | Arc length |
| [Circumference Calculator](/math/circumference/) | i know the and value | Circumference |
| [Diameter to Radius Calculator](/math/diameter-to-radius/) | diameter | Diameter to Radius |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Value must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
What is the radius of a circle with area 100?
For an area of 100, r = √(100 ÷ π) ≈ 5.642.
How do I find the radius from a chord?
You also need the sagitta or angle.
Is the radius half the diameter?
Yes. The radius is always half the diameter, so a 9 cm diameter has a 4.5 cm radius.
What does the Radius Calculator calculate?
Radius of a circle from diameter, circumference or area. It returns Radius, Diameter, Circumference and Area.
What formula does the Radius Calculator use?
d = 2r; C = 2πr; A = πr². Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
What does the “I know the” option change?
It sets how the radius is worked out. The choices are Radius, Diameter, Circumference and Area.
What is an example of a radius result?
With i know the Diameter and value 9, the radius is 4.5.
Related calculators
- Circle Diameter Calculator — Diameter of a circle from radius, circumference or area.
- Sector Area Calculator — Area and arc length of a circular sector.
- Arc Length Calculator — Length of a circular arc.
- Circumference Calculator — Circumference of a circle.
- Diameter to Radius Calculator — Convert a circle's diameter to its radius.
- Circumference to Radius Calculator — Convert a circle's circumference to its radius.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.