IEEE-754 Float Converter
Number ↔ float32 bit pattern with sign/exponent/mantissa split — see exactly why 0.1 + 0.2 ≠ 0.3.
IEEE-754 Float Converter computes float32 numbers ↔ bit patterns, split into sign, exponent and mantissa — free, instant and private in your browser. Embedded and systems developers debugging float behaviour and binary dumps use it to skip the datasheet algebra: type your numbers, read the answer with the substituted formula shown step by step, and share an exact permalink of the calculation.
About IEEE-754 Float Converter
IEEE-754 Float Converter computes float32 numbers ↔ bit patterns, split into sign, exponent and mantissa using the standard engineering relation: value = (−1)^s · 1.m · 2^(e−127); e=0 subnormal, e=255 Inf/NaN. Worked live: 3.14159 stores as 0x40490FD0 — and decodes back to 3.1415899, not your decimal. The result recalculates on every keystroke, the worked-example panel shows your numbers substituted into the formula, and the Copy permalink button encodes the inputs in the URL so a colleague opens exactly your calculation. Everything runs client-side — nothing you type leaves your device.
How to use IEEE-754 Float Converter
- 1Enter your values — the tool starts with realistic defaults for this exact use case, so the worked example is meaningful immediately.
- 2Read the live result and the worked-example panel, which substitutes your numbers into the formula step by step.
- 3Adjust any input to compare scenarios, then use Copy result or Copy permalink to share the calculation.
Why use IEEE-754 Float Converter?
- ✓Implements the real formula — value = (−1)^s · 1.m · 2^(e−127) — with the substitution shown, not a black box
- ✓Built for embedded and systems developers debugging float behaviour and binary dumps
- ✓Copy result and permalink buttons — share the exact calculation in a README, forum answer or design review
- ✓100% free, no sign-up, runs entirely in your browser (works offline once loaded)
Frequently asked questions
How do you calculate ieee-754 float?+
Float32 numbers ↔ bit patterns, split into sign, exponent and mantissa follows value = (−1)^s · 1.m · 2^(e−127); e=0 subnormal, e=255 Inf/NaN. For example, 3.14159 stores as 0x40490FD0 — and decodes back to 3.1415899, not your decimal. The calculator applies the same relation and shows the substituted arithmetic so you can verify every step.
Why doesn't 0.1 + 0.2 equal 0.3 in floating point?+
None of those decimals is exactly representable in binary — each stores as the nearest of 2²³ mantissa steps, and the rounding residues don't cancel. Compare with a tolerance (|a−b| < ε), never ==, and use integers or decimal types for money.
How many digits can float32 actually hold?+
About 7 significant decimal digits. Accumulating many small increments into a large float silently loses them once the magnitude gap exceeds 2²³ — sensor totalisers and long-running timers should accumulate in int64 or float64 instead.
Is the IEEE-754 Float Converter free and private?+
Yes — completely free with no sign-up or usage limits, and it runs entirely in your browser: the values you enter are never uploaded or stored on a server.
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