Technology & Computing
IEEE 754 Floating Point Precision Calculator
Show the mantissa/exponent bit split, machine epsilon and representable range for IEEE 754 single or double precision.
Your inputs
Change any value to update the result instantly.
Machine epsilon
0
Mantissa bits
52 bits
Exponent bits
11 bits
Max representable value
17,97,69,31,34,86,23,15,70,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,00,000
Min normal positive value
0
Decimal digits of precision
15.6536 digits
Double precision gives about 15-17 significant decimal digits.
Formula and working
Machine epsilon = 2^-mantissaBits; Max value ≈ 2^(2^(expBits-1)) × (2 - epsilon); Decimal digits ≈ mantissaBits × log10(2)
- 1
Collect the inputs
Precision format = 64
- 2
Apply the formula
Machine epsilon = 2^-mantissaBits; Max value ≈ 2^(2^(expBits-1)) × (2 - epsilon); Decimal digits ≈ mantissaBits × log10(2)
- 3
Result
Machine epsilon = 0
Frequently asked questions
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
Report a mistake or request an improvement
Tell us if a formula, unit, explanation, or result needs attention. Your message will include this calculator’s name and page.
Related calculators
Binary, Octal, Decimal & Hexadecimal Multi-Base Converter
Convert a decimal number into binary, octal and hexadecimal representations and see its bit length.
Hash Collision Probability & Birthday Attack Calculator
Estimate the probability of a hash collision occurring among a set of hashed items, based on the birthday paradox.
Text Encoding Byte Size Calculator
Estimate the storage size in bytes of a text string under ASCII, UTF-8, UTF-16 and UTF-32 encodings.
Two's Complement Signed Integer Range Calculator
Find the two's complement binary/hex encoding of a signed value and the representable range for a given bit width.
AES-GCM Nonce Collision & Key Exhaustion Calculator
Estimate the safe number of messages encrypted under one AES-GCM key before random 96-bit nonce collisions become likely.
DNS TTL Propagation Window Calculator
Estimate the worst-case and average time for a DNS record change to propagate across caching resolvers based on TTL.