Circle Area Calculator

πr², where r is the radius. If you have the diameter, halve it first — using the diameter directly gives four times the correct area.

2πr, or πd if you have the diameter. The ratio of circumference to diameter is π for every circle, which is what makes π a constant.

78.54%, which is π/4, regardless of size. It is why a round pizza in a square box always looks wasteful and why circular ducts carry more air than square ones of the same width.

Half the circle's area, πr²/2. The perimeter is not half the circumference, though — it is half the circumference plus the diameter, since the straight edge is now a boundary.

Divide by π and take the square root. An area of 78.54 gives a radius of 5.

It cannot be written as a fraction of two integers, which was proved in 1761. Its decimal expansion never terminates or repeats, which is why every numerical value of π is an approximation.

The outer circle's area minus the inner one: π(R² − r²). It is the shape of a washer or a ring, and the formula is simpler than it looks.

The fraction of the full circle it covers, so πr² times the angle over 360 degrees — or half r squared times the angle in radians, which is why radians are cleaner.

The sector area minus the triangle formed by the two radii and the chord. It is the calculation needed for liquid in a cylindrical tank lying on its side.

Fifteen decimal places is enough to calculate the circumference of the observable universe to the width of a hydrogen atom. For anything practical, three or four suffice.

By inscribing and circumscribing polygons and squeezing the value between them — Archimedes reached 96 sides. Infinite series replaced the method in the seventeenth century.

Because the area formula can be derived by cutting a circle into thin sectors and rearranging them into a near-rectangle of width πr and height r. The same constant appears because it is the same circle.