About the IEEE 754 Converter
IEEE 754 is the standard way computers store numbers with a decimal point. This converter shows the 32-bit (float) or 64-bit (double) representation of a number, split into the sign bit, the exponent bits and the mantissa bits, with the hex code and the exact value actually stored. It can also turn 8 or 16 hex digits back into a number. Type a decimal number or hex digits and the IEEE 754 float appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the IEEE 754 Converter
- 1Enter a decimal number or hex digits.
- 2Pick the units or options from the menus if the IEEE 754 float tool offers them.
- 3Read the IEEE 754 float in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the IEEE 754 float
Programmers use it to understand why 0.1 + 0.2 is not exactly 0.3, to debug binary files and to learn how numbers are stored.
Many decimal fractions, such as 0.1, have no exact binary form, so the stored value is the nearest one. The tool shows that stored value so the small error is visible.
How the IEEE 754 float is worked out
A float is stored as (−1)^sign × 1.mantissa × 2^(exponent − bias). The bias is 127 for 32-bit and 1023 for 64-bit. 0.1 as a 32-bit float is 3DCCCCCD in hex, which is stored as 0.10000000149011612. As a 64-bit double it is 3FB999999999999A.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Sign, exponent, mantissa
- 32 and 64 bit
- Reads hex back
Mistakes to avoid with IEEE 754 float
Choose 32 or 64 bit before converting. Special values are handled: zero, infinity and not-a-number have their own bit patterns.
On phone and computer
On a phone, type into the boxes one after another and read the IEEE 754 float underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the IEEE 754 float move. The ieee 754 converter works the same on both.
Checking your IEEE 754 float by hand
A good habit is to test the ieee 754 converter with a case you already know. 0.1 as a 32-bit float is 3DCCCCCD in hex, which is stored as 0.10000000149011612. As a 64-bit double it is 3FB999999999999A.
If your own figures give a surprising answer, repeat the working yourself: A float is stored as (−1)^sign × 1.mantissa × 2^(exponent − bias). The bias is 127 for 32-bit and 1023 for 64-bit. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. Floating point bits make more sense next to other binary forms. Look at signed integers with the Two's Complement Calculator, write numbers in ones and zeros with the Binary Translator, and do bitwise sums with the Binary and Hex Calculator.
Features
- Stored value may differ slightly
- Pick the format first
- Special values handled
- Clear messages when the IEEE 754 float inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate IEEE 754 float?
A float is stored as (−1)^sign × 1.mantissa × 2^(exponent − bias). The bias is 127 for 32-bit and 1023 for 64-bit. 0.1 as a 32-bit float is 3DCCCCCD in hex, which is stored as 0.10000000149011612. As a 64-bit double it is 3FB999999999999A.
What is the formula for IEEE 754 float?
A float is stored as (−1)^sign × 1.mantissa × 2^(exponent − bias). The bias is 127 for 32-bit and 1023 for 64-bit. The ieee 754 converter applies it exactly and rounds only the displayed answer to six significant figures.
Why is 0.1 not exact?
Because 0.1 is a repeating fraction in binary.
What is the bias?
A constant added to the exponent so it can be stored without a sign.
What is NaN?
Not a number, the result of undefined operations such as 0 ÷ 0.
Is this ieee 754 converter free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.