A circle is every point at one fixed radius from its center. Radius, angle, and the constant π connect its lengths and areas.
Use it to move between a circle’s central measurements while keeping the radius and angle units explicit.
The relationship
Write the rule before calculating
A = πr², C = 2πr, d = 2r
See the structure
What the calculation is doing
centerrθA = πr², C = 2πr, d = 2r
Worked interpretation
Read the result in context
Enter the example values shown in the fields to verify the stated relationship.
Interpret with care
Important boundary
Use radians in arc and sector formulas unless the degree angle is explicitly converted first.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Understand the subject
What defines a circle?
A circle is every point in a plane at the same distance—its radius—from one center.
Use a known radius to connect the circle’s diameter, circumference, and area.
The relationship
The defining equation
d=2r, C=2πr, A=πr²
r is the entered radius, d diameter, C circumference, and A area.
See the structure
Linear scaling and area scaling differ
Radius sets both circumference and area
Worked example
Circle with radius 3
d=6, C=6π≈18.85, A=9π≈28.27
Interpret with care
What the result does—and does not—mean
Circumference uses length units; area uses square units. π-based decimal results are approximations.
Quick guide
How to use this calculator
Enter values using the notation shown beside each field.
Choose a calculation mode when the tool offers more than one interpretation.
Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
A = πr², C = 2πr, d = 2r
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
Enter the example values shown in the fields to verify the stated relationship.
A = πr², C = 2πr, d = 2r
Supported inputs
Precision and limits
Finite, bounded input
Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.
Notation
Lengths are unit-neutral but must use one consistent unit throughout a calculation. Angles are entered in degrees where labelled.
