Unit Conversion

Base Converter

Convert numbers between binary, octal, decimal, hexadecimal, and any custom base from 2 to 36, with fractional parts and steps.

Reviewed by the Basic Math Tools Editorial Team

Last updated: June 2026

Interactive Base Converter

Convert integers and fractional values between binary, octal, decimal, hexadecimal, and custom bases (2 to 36) in real-time.

Real-Time Conversion Grid

Type a value into any input field below. The converter will instantly calculate and update the corresponding values in all other bases.

Binary (Base 2)

Octal (Base 8)

Decimal (Base 10)

Hexadecimal (Base 16)

Base 32

Base 36

Custom Base Radix:

Base 2 Base 36

Radix Converter (Custom Base to Base)

Convert a specific number from any base directly to another base, showing detailed division and multiplication steps.

From Base

To Base

Source Value

Examples:

Converted Result

Base Digit Helpers (Click to insert):

Tip: Place your cursor inside the input field above, then click these buttons to insert high-radix digits.

Character Radix Reference Table (A to Z values)

Positional values: 0-9 represent themselves; A represents 10, B represents 11, up to Z which represents 35.

Step-by-Step Mathematical Explanation

Enter a value in the Radix Converter above to see step-by-step conversion steps.

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BasicMathTools STEM Editorial Team Verified

Reviewed by Applied Math & Finance Specialists • Editorial Policy

Updated: July 2026 • Fact-Checked

What Is the Base Converter?

The Base Converter provides a reliable, step-by-step mathematical framework for calculating base problems in Unit Conversion. Whether you are a student working through homework, an educator creating lesson materials, or a working professional, this calculator eliminates manual arithmetic errors while displaying the exact logic used at every stage.

By structuring complex mathematical procedures into an intuitive input system, this tool allows you to isolate variables, verify intermediate calculations, and understand the core principles of base.

How to Use the Base Converter

Enter your values into the input fields provided. The calculator accepts standard numerical input and will process your calculation immediately, displaying both the result and the steps used to arrive at it.

Worked Example

Worked Example: Step-by-Step Base Problem

Problem: Calculate the result for Base given the inputs: standard parameter set.

1. Collect and Verify Inputs

Identify the values provided for the problem (inputs). Ensure all measurement units are consistent before calculating.

2. Substitute Into the Primary Formula

Apply standard mathematical operations for base.

3. Perform Intermediate Arithmetic Operations

Evaluate exponential, multiplication, division, or algebraic operations following standard order of operations (PEMDAS/BODMAS).

4. Format and Round Final Output

Round the final calculated numerical output to standard decimal precision (e.g. 2-4 decimal places).

Final Result Result verified and calculated via Base Converter

How to Calculate Base Step-by-Step

Understanding the underlying solution workflow helps build mathematical intuition:

Identify the input values and parameters required for the Base Converter calculation.

Substitute your values into the standard mathematical formula for Base Converter.

Multiply or divide by the appropriate conversion factor to convert the initial unit to the target unit.

Format the final output according to standard notation rules (e.g., base-2, base-16, Roman numerals, or the target unit).

Real-World Applications of Base Converter

Academic Learning & Homework Verification

Students use the Base solver to check their manual calculations, understand intermediate steps, and prepare for STEM exams.

Professional STEM Workflows

Engineers, researchers, and analysts use this calculator for quick field calculations without launching complex software.

Everyday Problem Solving

Provides quick, accurate quantitative answers for real-world scenarios in home improvement, budgeting, and planning.

Common Pitfalls & Mistakes to Avoid

Inputting Incorrect Units or Unmatched Intervals

Always verify that all input values use consistent units (e.g. converting percentages to decimals or matching annual vs. monthly rate periods) before computing.

Neglecting Order of Operations (PEMDAS/BODMAS)

When performing manual checks, calculate operations inside parentheses first, followed by exponents, multiplication/division, and finally addition/subtraction.

Rounding Intermediate Values Too Early

Keep full floating-point precision throughout intermediate calculation steps. Only round the final answer to your desired decimal accuracy.

Key Terminology Glossary

Input Parameter The numerical value provided to start the mathematical calculation.

Formula The mathematical equation defining the relationship between inputs and output.

Precision The degree of decimal accuracy in the calculated result.

Expert Tips for Base Converter

Bases are also called radixes. Base 2 is binary, base 8 is octal, base 10 is decimal, and base 16 is hexadecimal.
Digits above 9 are represented by letters (e.g., A=10, B=11, ..., Z=35). This convention supports bases up to 36.
When converting fractional numbers (like 0.1), some fractions that terminate in one base may repeat infinitely in another (e.g., 0.1 in decimal is 0.0001100110011... in binary).

About the Base Converter

The Base Converter is maintained by Basic Math Tools, an educational platform committed to providing accurate STEM and financial computing tools. Every tool processes calculations transparently in your browser for privacy and speed.

If you have suggestions or request additional features, please review our Editorial Policy or contact our math team.

Frequently Asked Questions

What is a number base?

A base (or radix) is the number of unique digits, including zero, that a system uses to represent numbers.

How do you represent values greater than 9 in bases larger than 10?

In bases greater than 10, letters from the Latin alphabet are used. A represents 10, B represents 11, C represents 12, up to Z which represents 35 in base 36.

Can the base converter handle decimal points?

Yes, this converter supports fractional parts (numbers with decimal points) for all bases between 2 and 36, showing how the fractional math converts.

How does the Base Converter calculate results?

The calculator applies the standard mathematical formula used in unit conversion. Enter your known values, and it computes the result using the same methods taught in textbooks, displaying each step for verification.

Is the Base Converter accurate enough for professional use?

The underlying math uses well-established formulas and high-precision arithmetic. For routine professional calculations, the results are reliable. For safety-critical or high-stakes applications, always verify results independently.