Quick answer
Radius = diameter ÷ 2. A diameter of 10 gives a radius of 5.
Enter the diameter. The calculator returns the radius.
Related tools: Radius Calculator: Radius of a circle from diameter, circumference or area. Circle Diameter Calculator: Diameter of a circle from radius, circumference or area. Circumference to Diameter Calculator: Convert a circle's circumference to its diameter.
How to use the Diameter to Radius Calculator
- Enter diameter (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Diameter | A number | > 0 |
Formula and method
Formula
r = d ÷ 2
IEEE-754 double precision; shown to at most 6 decimal places.
Direct application of the circle relationships.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Diameter = 10.
| Result | Value |
|---|---|
| Diameter to Radius | 5 |
Example 2
Inputs: Diameter = 7.
| Result | Value |
|---|---|
| Diameter to Radius | 3.5 |
The first line is the headline result (diameter to Radius). IEEE-754 double precision; shown to at most 6 decimal places.
The simplest circle conversion
The diameter passes through the centre; the radius runs from the centre to the edge, half as long. Tools and pipes are specified by diameter, while formulas usually use radius.
Next steps
From the radius, area is πr² (78.54 for r = 5) and circumference 2πr (31.42). Halve the diameter before using area or volume formulas, since using d instead of r is a classic error.
Radius or diameter
The radius is half the diameter: 10 becomes 5 and 7.5 becomes 3.75. A 12-inch pizza has a radius of 6 inches.
Use the radius, not the diameter, in the area formula πr².
How the result changes with diameter
Holding every other input at the first worked example, this table changes only diameter. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Diameter | Diameter to Radius |
|---|---|
| 5 | 2.5 |
| 10 | 5 |
| 20 | 10 |
| 40 | 20 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Diameter: entering "0" shows "Diameter must be greater than 0." beside that field and no result.
Choosing between the Diameter to 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 |
|---|---|---|
| [Radius Calculator](/math/radius-calculator/) | i know the and value | Radius |
| [Circle Diameter Calculator](/math/circle-diameter/) | i know the and value | Diameter |
| [Circumference to Diameter Calculator](/math/circumference-to-diameter/) | circumference | Circumference to Diameter |
| [Circumference to Radius Calculator](/math/circumference-to-radius/) | circumference | Circumference to Radius |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
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 diameter to confirm this.
Frequently asked questions
What radius has a diameter of 7?
A diameter of 7 gives a radius of 3.5.
Is the radius always half?
Yes. Every diameter is exactly twice the radius, so r = d ÷ 2 for any circle.
Why do formulas use the radius?
It's the natural parameter of a circle.
What is the radius of a 12-inch pizza?
6 inches.
Which do I use in the area formula?
The radius. Halve the diameter first.
What does the Diameter to Radius Calculator calculate?
Convert a circle's diameter to its radius. It returns Diameter to Radius.
What formula does the Diameter to Radius Calculator use?
r = d ÷ 2. Direct application of the circle relationships.
What do I need to enter in the diameter to Radius Calculator?
You enter Diameter.
What is an example of a diameter to Radius result?
With diameter 10, the diameter to Radius is 5.
Related calculators
- Radius Calculator — Radius of a circle from diameter, circumference or area.
- Circle Diameter Calculator — Diameter of a circle from radius, circumference or area.
- Circumference to Diameter Calculator — Convert a circle's circumference to its diameter.
- 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.