Pi (π) is the ratio of a circle's circumference to its diameter, approximately 3.14159265358979. It is irrational and transcendental — its decimal expansion never repeats and never terminates.

What is Euler's number e?

Euler's number e ≈ 2.71828 is the base of the natural logarithm. It arises naturally in compound interest, probability, and calculus. It is irrational and transcendental like Pi.

Math Constants — Pi, e, Phi, Tau Digits

Mathematical constants are fundamental values that appear throughout mathematics and physics. Pi (π), Euler's number (e), the Golden Ratio (φ), and Tau (τ) are among the most important and famous. These constants are irrational — their decimal expansions are infinite and never repeat in a predictable pattern.

Famous Mathematical Constants

π (Pi): 3.14159265... — ratio of circle circumference to diameter
e (Euler's number): 2.71828182... — base of natural logarithm
φ (Golden Ratio): 1.61803398... — appears in art, nature, and Fibonacci sequences
τ (Tau): 6.28318530... — 2π, the ratio of circumference to radius
√2 (Pythagoras' constant): 1.41421356... — diagonal of unit square
√3 (Theodorus' constant): 1.73205080...
ln 2: 0.69314718... — natural log of 2
γ (Euler–Mascheroni): 0.57721566... — limiting difference between harmonic series and natural log

Frequently Asked Questions

How many digits of Pi have been computed?

As of 2024, over 100 trillion digits of Pi have been computed. This tool displays up to 1,000 digits from a stored high-precision value.

Why is Pi irrational?

Pi is irrational, meaning it cannot be expressed as a fraction of two integers. This was proved by Johann Lambert in 1768. Pi is also transcendental (proved by Ferdinand von Lindemann in 1882), meaning it is not the root of any polynomial with rational coefficients.

Math Constants online

Digits of Pi, e, Golden Ratio, Tau, and other mathematical constants — runs in your browser

Famous Mathematical Constants

Frequently Asked Questions

How many digits of Pi have been computed?

Why is Pi irrational?