What is the formula for the Circle Calculator?
Circle Calculator: diameter = 2r; area = πr²; circumference = 2πr. Input definitions: mode = Known measurement; value = Known value. Use the selected convention throughout the calculation.
Plane geometry
Circle Calculator
Calculate radius, diameter, area and circumference from one known circle measurement. The selected measurement determines whether the input is a length or an area.
- Explicit formulas and worked examples
- Check your inputs, then calculate
- Data is calculated in this browser only
Check the stated input format, calculation convention and limits before using the result.
Check the example inputs, then calculate. Your values stay in this browser.
The input must be positive.
Calculation notes
Understand the Circle Calculator
Circle Calculator validates known measurement, known value before applying the displayed equation. The input must be positive.
How can I reproduce the Circle Calculator example?
Circle Calculator baseline input: Known measurement: Radius; Known value: 3. Output: Radius = 3; Diameter = 6; Area = 28.274333882308; Circumference = 18.849555921539. Substitute these values into the displayed equation to reproduce the result.
How should I interpret the Circle Calculator result?
- Read radius with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
What limits apply to the Circle Calculator?
- The input must be positive.
- π-based outputs are numerical approximations; units are not inferred automatically.
Content and calculation reviewed:
Understand the calculation
How to use it and the math behind it
Four steps to check your inputs and results
- Calculate radius, diameter, area and circumference from one known circle measurement. The selected measurement determines whether the input is a length or an area.
- Enter Known measurement, Known value in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read radius with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. The input must be positive. π-based outputs are numerical approximations; units are not inferred automatically.
Circle Calculator: calculation relationships
Selecting area reverses πr²: divide by π and then take the square root. An area of 4π gives radius 2, diameter 4 and circumference 4π. Selecting circumference instead divides by 2π without a square root. Keep the squared input unit for area distinct from the linear input unit used for radius, diameter and circumference.
diameter = 2r; area = πr²; circumference = 2πr
The detailed guide adds variable definitions, a reproducible example, a practice question and model limitations.
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