Circle Area Calculator

Enter a circle radius to calculate the exact area in terms of π and a decimal approximation, with the formula A = πr² shown step by step.

Circle area calculator using radius squared times pi

Use this circle area calculator when a problem gives the radius and asks for π times the radius squared.

The result keeps π in the exact form first, then shows a decimal approximation in square units.

Examples include decimal radii such as 4.89 and 7.6, where rounding too early can noticeably change the area.

Features

  • Direct radius input for whole numbers and decimals.
  • Exact result written as a multiple of π.
  • Decimal area approximation in square units.
  • Visible radius-squared and multiplication steps.
  • Quick examples for common πr² calculations.

Example expressions

  • r = 4.89
  • r = 7.6
  • r = 1.4
  • r = 2.5
  • r = 31
  • r = 47

Example problems with answers

r = 4.89
The exact area is 23.9121π, approximately 75.122956 square units.
r = 7.6
The exact area is 57.76π, approximately 181.458392 square units.
diameter = 10
The radius is 5, so the area is 25π, approximately 78.539816 square units.

Related formulas

  • Circle area: A = πr².
  • If the diameter is d, then r = d/2.
  • Area units are squared, such as cm² or m².
  • Keep the full radius before squaring to avoid early rounding error.

How to use this calculator

  1. Enter the radius, not the diameter.
  2. Square the complete radius value.
  3. Multiply the squared radius by pi.
  4. Read the exact π result and the decimal approximation.
  5. Attach squared units that match the radius unit.

Common input mistakes

  • Do not use the diameter as the radius; divide the diameter by 2 first.
  • Square the radius before multiplying by pi.
  • Do not round a decimal radius before squaring it.
  • Area uses square units, not ordinary length units.
  • A negative radius is not a valid geometric input.

FAQ

What is the formula for the area of a circle?

The formula is A = πr², where r is the circle radius.

Can I enter a decimal radius?

Yes. Enter the complete decimal value and the calculator will square it before multiplying by pi.

What if I only know the diameter?

Divide the diameter by 2 to get the radius, then enter that radius.

Why is the result written with pi and as a decimal?

The π form is exact, while the decimal is an approximation that is convenient for measurements.

What units should I use for the answer?

Use the square of the radius unit. A radius in centimeters produces an area in square centimeters.

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