Hexadecimal Calculator

This professional hex calculator performs high‑precision hexadecimal arithmetic and fast base conversions. It is designed for students, engineers, and developers who need reliable calculations, clear steps, and accessible UX. Enter values to add, subtract, multiply, divide, or convert between hex, decimal, binary, and octal.

Calculator

Mode
Use 0–9 and A–F (case‑insensitive). Optional leading 0x is allowed. Negative sign is supported.
Division returns quotient and remainder
Same format as Operand A. For division by zero, an error will be shown.
Ready

Results

Enter values and choose an action. Results will appear here with step-by-step details.

Data Source and Methodology

Authoritative reference: ISO/IEC 80000‑2:2019 — Quantities and units — Part 2: Mathematics. ISO, 2019. Official ISO page. Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The calculator implements standard positional numeral system algorithms for base‑16 arithmetic using arbitrary‑precision integers to avoid rounding errors.

The Formula Explained

Value of a hexadecimal numeral:
$$N = \sum_{i=0}^{k-1} d_i \cdot 16^i,\quad d_i \in \{0,\dots,9,A,\dots,F\}$$
Addition/Subtraction in base 16 (with carry/borrow):
$$\forall i:\ s_i = a_i \oplus b_i \oplus c_{i},\quad c_{i+1} = \left\lfloor\frac{a_i + b_i + c_{i}}{16}\right\rfloor$$
Multiplication (schoolbook):
$$A \times B = \sum_{i=0}^{m-1}\sum_{j=0}^{n-1} a_i b_j \cdot 16^{i+j}$$
Integer division with remainder:
$$A = B \cdot Q + R,\quad 0 \le R < |B|$$

Glossary of Variables

  • Operand A, Operand B: Input hexadecimal integers (accepts optional 0x prefix and a leading minus sign).
  • Operation: Arithmetic operation in base 16: Add, Subtract, Multiply, Divide.
  • Result (Hex): Primary output in uppercase hexadecimal.
  • Quotient, Remainder: Outputs for division in hex.
  • Decimal, Binary, Octal: Equivalent values in bases 10, 2, and 8.
  • Auto-detect: Recognizes prefixes 0x (hex), 0b (binary), 0o (octal); otherwise assumes the selected base.

How It Works: A Step‑by‑Step Example

Suppose you want to compute 1A3F + 2B.

  1. Convert each to decimal: 1A3F = 1×16³ + 10×16² + 3×16¹ + 15 = 4096 + 2560 + 48 + 15 = 6719; 2B = 2×16¹ + 11 = 43.
  2. Add in decimal: 6719 + 43 = 6762.
  3. Convert 6762 back to hex: 6762 = 1A6A.
  4. Binary check: 1A6A = 0001 1010 0110 1010₂.

Therefore, the result is 1A6A (hex).

Frequently Asked Questions (FAQ)

What characters are valid in hexadecimal?

Digits 0–9 and letters A–F (case‑insensitive). An optional 0x prefix and a leading minus sign are supported.

How does the calculator handle very large numbers?

It uses arbitrary‑precision integers (BigInt) for exact arithmetic. There is no fixed bit‑width limit like 32‑ or 64‑bit integers.

Is there any rounding?

No. All operations are integer‑exact. Division returns both quotient and remainder.

Can I paste values with spaces or underscores?

Yes. Spaces and underscores are ignored in inputs for readability.

Does the tool support bitwise operations?

Not yet. Our focus is precise arithmetic and conversions. Bitwise operators are on the roadmap.

Why are results displayed in uppercase?

Uppercase hex (A–F) is a widely accepted convention that improves readability and consistency.

Strumento sviluppato da Ugo Candido. Contenuti verificati da CalcDomain Editorial Team.
Ultima revisione per l'accuratezza in data: .