Octal to Decimal converter
Convert octal (base 8) to decimal (base 10). Formula: sum digit × 8ⁿ. Runs locally in your browser. Free online tool — no sign-up. Fast and free.
Enter values to convert.
Formulas
Core equations used by this converter.
How to use
Write the octal number and number positions from the right s
Write the octal number and number positions from the right starting at 0.
Multiply each digit by 8 raised to its position.
Multiply each digit by 8 raised to its position.
Add the products.
Digits 8 and 9 are invalid in octal.
Example conversions
Common values with formula and result.
Example 1: 37₈ → decimal
Example 1: 37₈ → decimal
Example 2: 7014₈ → decimal
Example 2: 7014₈ → decimal
Example 3: 10₈ → decimal
Example 3: 10₈ → decimal
Reverse check: 31₁₀ should be 37₈
Reverse check: 31₁₀ should be 37₈
Octal to Decimal converter specification
Version 1.1.0 · Engine tested
- Engine tested 4 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- **Octal (base 8)** — digits **0–7** only. Place values are powers of 8. Historically used in computing (each digit maps to 3 bits). **Decimal (base 10)** — everyday base with digits 0–9.
- What it calculates
- Convert octal (base 8) to decimal (base 10). Formula: sum digit × 8ⁿ. Worked examples and an octal↔decimal chart.
- Inputs
- Values required by the selected conversion mode
- Outputs
- Converted result in the target unit or format
- Formula
decimal = dₙ×8ⁿ + … + d₁×8¹ + d₀×8⁰- Octal to decimal conversion table
Octal (base 8) Decimal (base 10) 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 10 8 11 9 12 10 17 15 - 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
- Example 1: 37₈ → decimal → 31₁₀
- Validation cases
- Example 1: 37₈ → decimal → 31₁₀
- Example 2: 7014₈ → decimal → = 3596₁₀
- Example 3: 10₈ → decimal → 8₁₀
- Reverse check: 31₁₀ should be 37₈ → 37₈ ✓
- 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 Octal to Decimal converter update locally in your browser.
Related tools
Frequently asked questions
Key distinctions behind the conversion.
How do you convert using Octal to Decimal converter?
Use decimal = dₙ×8ⁿ + … + d₁×8¹ + d₀×8⁰. Example: Example 1: 37₈ → decimal → 31₁₀.
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.