Circle Calculator
Enter any one of the radius, diameter, circumference or area of a circle and get the other three. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates radius, diameter, circumference and 1 more result from the value you know and value. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Use this to find the cross-sectional area of a solid round conductor or a pipe from its diameter, the length of wire around a drum or a coil turn, or the diameter that gives a required area. For wire gauges use the AWG and SWG converters, which also give the diameter and area of standard sizes.
Cross-check: 32 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 32 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| The value you know | Radius |
| Value | 5 |
- Known: radius = 5
- Radius r = 5 Diameter d = 2r = 10
- Circumference = 2πr = 31.4159265359
- Area = πr² = 78.5398163397
Assumptions
- The shape is a perfect circle
- Only the one value chosen is used; the others are worked out from it
- The tool works on plain numbers and does not track units: area is in the unit of length squared, so a diameter in mm gives an area in mm²
- For a stranded conductor the area found here is that of a solid round conductor of the same diameter, which is more than the copper area
- π is taken to full double-precision accuracy
Use this to find the cross-sectional area of a solid round conductor or a pipe from its diameter, the length of wire around a drum or a coil turn, or the diameter that gives a required area. For wire gauges use the AWG and SWG converters, which also give the diameter and area of standard sizes.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| The value you know | (choice) | Radius; Diameter; Circumference; Area | |
| Value | (number) | 0 or more, up to 1,000,000,000,000 | The size of the quantity chosen above, above zero, in one consistent unit (area in that unit squared). |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Radius | (number) | Shown to 10 decimal places | |
| Diameter | (number) | Shown to 10 decimal places | |
| Circumference | (number) | Shown to 10 decimal places | |
| Area | (number) | Shown to 10 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with value
| Value | Radius | Diameter | Circumference |
|---|---|---|---|
| 0.5 | 0.5 | 1 | 3.1415926536 |
| 1.25 | 1.25 | 2.5 | 7.853981634 |
| 2.5 | 2.5 | 5 | 15.7079632679 |
| 5 | 5 | 10 | 31.4159265359 |
| 10 | 10 | 20 | 62.8318530718 |
| 20 | 20 | 40 | 125.6637061436 |
| 50 | 50 | 100 | 314.159265359 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter the value you know and value. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
The shape is a perfect circle. Only the one value chosen is used; the others are worked out from it. The tool works on plain numbers and does not track units: area is in the unit of length squared, so a diameter in mm gives an area in mm². For a stranded conductor the area found here is that of a solid round conductor of the same diameter, which is more than the copper area. π is taken to full double-precision accuracy.
Which calculators should I use next?
Common next steps are Pythagorean Theorem (Right Triangle) Calculator, Triangle Calculator (Three Sides), AWG to Diameter and Area and SWG to Diameter and Area. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 32 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Conductor Resistance Formulas and Temperature: Conductor resistance formulas: resistance from length, area and resistivity, correction for temperature
- Cable Size Formulas: Current and Short-Circuit: Cable sizing formulas for current capacity with correction factors, conductor resistance and temperature
- Skin Effect Formulas: Skin Depth: Skin effect formulas: skin depth from resistivity and frequency for copper and aluminium
More Engineering Mathematics calculatorsAll engineering calculatorsCircle Calculator (Radius, Diameter, Circumference, Area) in Elecmetric