Here are some quick approximations for PI that I worked out:

PI = 3.141592653589793238462643383...


A) Multiply by 245, Divide by 78 = 3.1410256

- Error: 0.0005670 (0,018%)
- Fast: Both mult and division are single-byte calcs.


B) Multiply by 355, Divide by 113 = 3.14159292 (Standard)

- Error: 0.000000266 (0.0000085%)
- Very Accurate
- Standard Approximation used by many
- Although multiplication is double-byte the division is still single-byte


C) Multiply by 201, Divide by 64 = 3.140625

- Error: 0.0009677 (0.031%)
- Faster: Division can be done with six right-shifts


D) Multiply by 101, Divide by 32 = 3.15625

- Error: 0.01466 (0.467%)
- Faster: Division by five right-shifts


E) Multiply by 25, Divide by 8 = 3.125

- Error: 0.0166 (0.528%)
- Faster: Division by three right-shifts


F) Multiply by 13, Divide by 4 = 3.25

- Error: 0.1084 (3.45%)
- Fast: Division by two right-shifts


NOTE: If you have a constant for which you'd like an approximation, let me know.