π, e, φ, √2 and the other constants that keep turning up — each to 30 decimal places, with the definition, the symbol and where it appears.
Constants
10
Decimal places
30
π
3.14159…
e
2.71828…
π starts 3.141592653589793, e starts 2.718281828459045 and the golden ratio φ starts 1.618033988749894 — all three are irrational and have infinitely many decimals.
10 of 10 rows
| Symbol | Name | Value | 30 decimal places | Where it appears |
|---|---|---|---|---|
| π | Pi (circle constant) | 3.141592653590 | 3.141592653589793238462643383279 | Circumference and area of a circle, every wave and rotation |
| τ | Tau (2π) | 6.283185307180 | 6.283185307179586476925286766559 | One full turn in radians — the natural period of sine and cosine |
| e | Euler's number | 2.718281828459 | 2.718281828459045235360287471352 | Continuous growth, compound interest, the natural logarithm |
| φ | Golden ratio | 1.618033988750 | 1.618033988749894848204586834365 | The limit of the Fibonacci ratio; proportions in design and nature |
| √2 | Square root of 2 | 1.414213562373 | 1.414213562373095048801688724209 | The diagonal of a unit square; the DIN A paper aspect ratio |
| √3 | Square root of 3 | 1.732050807569 | 1.732050807568877293527446341505 | Height of an equilateral triangle; three-phase electrical systems |
| √5 | Square root of 5 | 2.236067977500 | 2.236067977499789696409173668731 | Appears inside the closed form of the golden ratio and Fibonacci |
| ln 2 | Natural log of 2 | 0.693147180560 | 0.693147180559945309417232121458 | Doubling time and half-life; the rule of 69 in finance |
| ln 10 | Natural log of 10 | 2.302585092994 | 2.302585092994045684017991454684 | Converting between natural and base-10 logarithms; decibels, pH |
| γ | Euler–Mascheroni constant | 0.577215664902 | 0.577215664901532860606512090082 | The gap between the harmonic series and the natural logarithm |
The “Value” column shows the number the way a computer stores it in double precision — roughly 15 to 17 significant digits. An ordinary floating-point number cannot hold more.
The 30-decimal column is stored as a string and is therefore independent of your device's arithmetic precision.
Every constant listed here is irrational: it cannot be written as a ratio of two whole numbers, and its decimal expansion neither terminates nor repeats.
Hover the chart to read the precise values.
All of them sit between 0.58 and 6.29 — unlike physical constants, mathematical ones are almost always numbers near unity.
Hover the chart to read the precise values.
Across only 30 places the counts vary a lot. Over millions of digits they even out — though an equal distribution has still never been proven.
Hover the chart to read the precise values.
After ten terms seven decimals are already correct. Factorials grow so fast that each further term barely changes anything.
The 30-place digit strings are the published decimal expansions from the OEIS entry for each constant, stored as strings so no floating-point rounding can touch them. The double-precision value shown beside each one is what your browser actually computes with.
Last checked against the sources on August 6, 2026.
π = 3.141592653589793238462643383279. Those digits are truncated, not rounded.
It means π cannot be written as a ratio of two whole numbers. 22/7 is therefore only an approximation — it is correct to two decimal places.
e is the sum of the series 1/0! + 1/1! + 1/2! + … and equally the limit of (1 + 1/n)ⁿ as n grows. It describes continuous growth and is the base of the natural logarithm.
Divide a Fibonacci number by its predecessor and the ratio approaches φ: 13/8 = 1.625, 21/13 ≈ 1.6154, 34/21 ≈ 1.6190. Exactly, φ = (1 + √5)/2.
τ is simply 2π, one full turn in radians. In formulas for circles and waves 2π appears so often that a symbol of its own shortens many expressions.
Very few. Fifteen decimals would give the circumference of the Earth to a fraction of a millimetre. The 30 places here are for reference, not for calculation.
From the ASCII table to SI prefixes and the physical constants — every lookup table in one place.
Open the Circle Calculator