High-Precision π Computation

An interactive demonstration computing π up to 100 decimal places

Set Calculation Parameters

Number of terms: 20
Precision (digits): 30

Calculation Results

π ≈ 3.14159...
3.14159...
Accuracy: 0 decimal places Computation time: 0ms

Convergence to π

Error Convergence

How This Formula Works

The formula provides an elegant way to compute π with relatively quick convergence:

\[\pi = 4(F(2) + F(3))\]

Where F(x) is an infinite series defined as:

\[F(x) = \frac{1}{x} - \frac{1}{3x^3} + \frac{1}{5x^5} - \frac{1}{7x^7} + \ldots\]

More generally, this can be written as:

\[F(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1) \cdot x^{(2n+1)}}\]

Term-by-Term Contributions

Term F(2) Value F(3) Value π Approx. Error