Determine the precision and representable range of a floating point format.
Floating point precision is relative, so the absolute gap between representable values grows with magnitude. Errors accumulate roughly as the square root of the operation count under random rounding. Money should never be held in binary floating point, because values like 0.1 have no exact representation and errors compound across arithmetic.
Floating Point Precision
Epsilon = 2 to the power of minus mantissa bits; digits = mantissa bits × log₁₀2
Epsilon = 2 to the power of minus mantissa bits; digits = mantissa bits × log₁₀2 Floating point precision is relative, so the absolute gap between representable values grows with magnitude. Errors accumulate roughly as the square root of the operation count under random rounding.
Money should never be held in binary floating point, because values like 0.1 have no exact representation and errors compound across arithmetic.
This calculator takes 3 inputs: Format width in bits, Magnitude of the value stored, Number of chained operations. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.