Enter the number of decimal places you want and explore digits of pi (π). This Pi Calculator displays pi to your chosen precision, calculates the circumference or area of a circle using π, and shows key pi facts. Enter a radius to compute circle measurements, or just explore pi's digits up to 100 decimal places.
Pi (π) to Selected Decimal Places
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Circumference (2πr)
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Circle Area (πr²)
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Diameter (2r)
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Common Pi Approximation
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Pi (π) is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159265358979. It is a mathematical constant that appears in countless formulas across geometry, physics, engineering, and statistics. Pi is irrational, meaning its decimal digits never repeat or terminate.
As of recent records, pi has been calculated to over 100 trillion decimal digits using supercomputers. For everyday calculations — engineering, science, or geometry — just 10 to 15 decimal places provide more than sufficient precision.
The circumference of a circle is calculated as C = 2πr, where r is the radius. Equivalently, C = πd where d is the diameter. For example, a circle with a radius of 5 units has a circumference of 2 × π × 5 ≈ 31.4159 units.
The area of a circle is A = πr², where r is the radius. For a circle with radius 5, the area is π × 25 ≈ 78.5398 square units. This formula is one of the most fundamental applications of π in geometry.
The most widely used simple approximation of pi is 22/7 ≈ 3.1428571, which is accurate to about 2 decimal places. A more precise fraction approximation is 355/113 ≈ 3.1415929, which is accurate to 6 decimal places and was known to ancient Chinese mathematicians.
Pi is an irrational number, which means it cannot be expressed as a simple fraction of two integers. Its decimal expansion is infinite and non-repeating. Pi is also transcendental, meaning it is not a root of any non-zero polynomial with rational coefficients.
Pi Day is celebrated on March 14 (3/14) each year, referencing the first three digits of pi: 3.14. The date was officially recognized by the U.S. House of Representatives in 2009. It coincides with Albert Einstein's birthday, making it doubly significant in scientific culture.
For most practical purposes, 5 to 10 decimal places of pi are more than sufficient. NASA uses only 15 decimal places of pi for its highest-precision space calculations. Using more digits beyond 15 has negligible effect on real-world accuracy.