Hex to Decimal Converter

How hexadecimal maps to decimal

Hexadecimal is a base-16 system. Its digits are 0 to 9 followed by a to f, where a is 10, b is 11, c is 12, d is 13, e is 14 and f is 15. Each position is worth a power of 16, starting with 1 on the right and then 16, 256, 4096, 65536 and so on.

decimal = dₙ × 16ⁿ + … + d₂ × 16² + d₁ × 16¹ + d₀ × 16⁰Each digit d runs from 0 to 15. Position 0 is the rightmost digit.

How to convert hex to decimal

1. Turn every letter into its number: a = 10 up to f = 15.
2. Number the digits from the right, starting at position 0.
3. Multiply each digit by 16 raised to its position.
4. Add all the products.

Example: convert 2f3. The digits are 2, 15 and 3, so the sum is 2 × 256 + 15 × 16 + 3 = 512 + 240 + 3 = 755.

Example with four digits: convert 1a3f. That is 1 × 4096 + 10 × 256 + 3 × 16 + 15 = 4096 + 2560 + 48 + 15 = 6719.

A familiar one: beef is 11 × 4096 + 14 × 256 + 14 × 16 + 15 = 45056 + 3584 + 224 + 15 = 48879.

What the converter accepts

• Digits 0 to 9 and letters a to f, in upper or lower case.
• No prefix, sign or point. An empty box, a 0x prefix, a minus sign, a dot or any other letter makes the answer box show NaN. Because e is a hex digit, 1e3 is read as the hex number 1e3, which is 483, and not as 1000.
• Exact up to 13 hex digits. The value is held as a double-precision number with 53 significant bits. Larger inputs are rounded, so 7fffffffffffffff, whose true value is 9223372036854775807, shows as 9223372036854776000.
• Very large results above 1e21 switch to exponent form, for example 7.555786372591432e+22.

Hex to decimal conversion table

Related conversions

The reverse direction is covered by the decimal to hex converter. To see the bits behind a hex value, use the hex to binary converter, and to add or multiply hex numbers without converting first, try the hexadecimal calculator.