Question

How might I go about calculating PI in C# to a certain number of decimal places?

I want to be able to pass a number into a method and get back PI calculated to that number of decimal places.

public decimal CalculatePi(int places)
{
    // magic
    return pi;
}

Console.WriteLine(CalculatePi(5)); // Would print 3.14159

Console.WriteLine(CalculatePi(10)); // Would print 3.1415926535

etc…

I don’t care about the speed of the program. I just want it to be as simple and easy to understand as it can be.

Answer 1

After much searching I found this little snippet:

public static class BigMath
{
    // digits = number of digits to calculate;
    // iterations = accuracy (higher the number the more accurate it will be and the longer it will take.)
    public static BigInteger GetPi(int digits, int iterations)
    {
        return 16 * ArcTan1OverX(5, digits).ElementAt(iterations)
            - 4 * ArcTan1OverX(239, digits).ElementAt(iterations);
    }

    //arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ...
    public static IEnumerable<BigInteger> ArcTan1OverX(int x, int digits)
    {
        var mag = BigInteger.Pow(10, digits);
        var sum = BigInteger.Zero;
        bool sign = true;
        for (int i = 1; true; i += 2)
        {
            var cur = mag / (BigInteger.Pow(x, i) * i);
            if (sign)
            {
                sum += cur;
            }
            else
            {
                sum -= cur;
            }
            yield return sum;
            sign = !sign;
        }
    }
}

It is working like a charm so far. You just have to add the System.Numerics library from the GAC to resolve the BigInteger type.