Number base converter
Convert integers between number bases (binary, octal, decimal, hex, and more). Use positional notation and divide-by-radix; examples for 2, 8, 10, 16.
Enter values to convert.
Formulas
Core equations used by this converter.
How to use
Open the converter
Use the interactive panel at the top of the page.
Enter values
Fill in the required fields for this conversion.
Convert and read the result
Use Convert or let the result update automatically.
Example conversions
Common values with formula and result.
Binary `110101` → decimal → hex
Binary `110101` → decimal → hex
Decimal `255` → binary and hex
Decimal `255` → binary and hex
Octal `17` → decimal
Octal `17` → decimal
Number base converter specification
Version 1.1.0 · Engine tested
- Engine tested 3 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- A **base** \(b\) uses digit values \(0 \ldots b-1\). Common bases: | Base | Name | Digits | | --- | --- | --- |
- What it calculates
- Convert integers between number bases (binary, octal, decimal, hex, and more). Use positional notation and divide-by-radix; examples for 2, 8, 10, 16.
- Inputs
- Values required by the selected conversion mode
- Outputs
- Converted result in the target unit or format
- Formula
decimal = d₀·b⁰ + d₁·b¹ + d₂·b² + … + dₙ₋₁·bⁿ⁻¹- Quick reference table
Base Name Digits 2 Binary 0, 1 8 Octal 0–7 10 Decimal 0–9 16 Hexadecimal 0–9, A–F - Assumptions
- Conversion runs locally in the browser; values are not uploaded.
- Uses the formulas documented on this page.
- Units
- Formula
- Boundary conditions
- Empty or invalid input yields no valid result.
- Out-of-range values may be rejected by the tool runtime.
- Example
- Binary `110101` → decimal → hex → = 32 + 16 + 4 + 1 = 53₁₀
- Validation cases
- Binary `110101` → decimal → hex → = 32 + 16 + 4 + 1 = 53₁₀
- Decimal `255` → binary and hex → 11111111₂
- Octal `17` → decimal → 15₁₀
- Sources
- CalculatorX converter runtime
- Standard unit / encoding definitions where applicable
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
Use the converter tabs to switch direction when available. Results for Number base converter update locally in your browser.
Related tools
Frequently asked questions
Key distinctions behind the conversion.
How do you convert using Number base converter?
Use decimal = d₀·b⁰ + d₁·b¹ + d₂·b² + … + dₙ₋₁·bⁿ⁻¹. Example: Binary `110101` → decimal → hex → = 32 + 16 + 4 + 1 = 53₁₀.
Can I switch direction?
Open the related reverse converter listed under Related tools.
Does this run online or locally?
Calculation runs locally in your browser. Values are not uploaded.
How precise are the results?
Results follow the formulas on this page. Round to the precision your use case needs.