Integer Type Range Calculator (int8 … int64)

Understanding the integer type range calculator — concept and principle

Fixed-width integer types such as int8, int16, int32 and int64 can hold only a limited range of values. Exceeding it causes overflow: the value wraps around, an error is raised, or (in C, for signed types) the behaviour is undefined. Pick a bit width to see the signed range, the unsigned maximum and how many decimal digits the largest value has, which helps when choosing a database column type, a file-format field or a variable for counters and IDs.

How it is calculated

• Signed (two's complement): −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1.
• Unsigned: 0 to 2ⁿ − 1.
• Decimal digits: floor(n × log₁₀ 2) + 1, the number of digits of the unsigned maximum 2ⁿ − 1 (log₁₀ 2 ≈ 0.30103).

Values are computed with exact big integers, so even 128-bit results are precise.

The principle

n bits can form 2ⁿ different patterns. Unsigned types assign them to 0 … 2ⁿ − 1. Two's complement gives the top bit a weight of −2ⁿ⁻¹ instead of +2ⁿ⁻¹, so half the patterns become negative. Zero takes one of the non-negative patterns, which is why the negative side has one more value than the positive side. Each bit is worth log₁₀ 2 ≈ 0.301 decimal digits, so 10 bits give about 3 digits (2¹⁰ = 1024 ≈ 10³).

Worked example

1. Input: 32 bits.
2. Signed minimum: −2³¹ = −2147483648. Signed maximum: 2³¹ − 1 = 2147483647.
3. Unsigned maximum: 2³² − 1 = 4294967295.
4. Digits: 32 × 0.30103 = 9.63, floor is 9, plus 1 = 10; indeed 4294967295 has 10 digits.

How to read the result

Reference points: int8 is −128 … 127 (uint8 up to 255), int16 is −32768 … 32767 (uint16 up to 65535), int64 tops out at 9223372036854775807, about 9.22 × 10¹⁸. A signed 32-bit counter of seconds overflows after about 68 years, which is the Year 2038 problem; a 32-bit ID column runs out at about 2.1 billion rows. For money, measurements or IDs that grow, choose a type with clear headroom.

Common mistakes

• Forgetting the asymmetry: −(−2147483648) does not fit in int32.
• Reading the digit count as the digits of the signed maximum; for 64 bits the unsigned maximum has 20 digits but the signed maximum has 19.
• Assuming C's int is always 32 bits; the standard only guarantees at least 16.
• Storing integers above 2⁵³ − 1 = 9007199254740991 in JavaScript numbers or JSON parsed as doubles, which silently loses precision.

Frequently asked questions

Why is the minimum −128 and not −127 for int8?

In two's complement, 10000000 means −128; there is only one zero, so one extra negative value remains.

How many bits do I need for a value N?

floor(log₂ N) + 1 bits unsigned, plus one sign bit if negatives are required.

Does Python have int64 limits?

Built-in Python integers have arbitrary precision; fixed limits apply only in libraries such as NumPy.

Sources: ISO/IEC 9899 (C standard), <stdint.h> exact-width integer types · Randal E. Bryant and David R. O'Hallaron, Computer Systems: A Programmer's Perspective, Pearson