BODMAS Calculator

Calculate mathematical expressions following the BODMAS order of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction) with step-by-step breakdown.

How to Use This Calculator

Enter your mathematical expression in the input field
Use + for addition, - for subtraction, × for multiplication, ÷ for division
Use ^ for powers (e.g., 2^3 for 2 to the power of 3)
Use parentheses ( ) to group operations
Adjust the decimal places slider for your desired precision
Click Calculate to see the result and step-by-step breakdown

BODMAS Order of Operations

B → O → D → M → A → S

Where:

B = Brackets (parentheses) - Operations inside brackets are calculated first
O = Orders (powers and roots) - Exponents and square roots are calculated next
D = Division - Performed from left to right
M = Multiplication - Performed from left to right
A = Addition - Performed from left to right
S = Subtraction - Performed from left to right

Example Calculation

Real-World Scenario:

You need to calculate the total cost of items with different prices and quantities, including tax and a discount.

Given:

Expression: 5 × (6 + 3) - 8 ÷ 2
5 items at $6 each with a $3 discount per item
Subtract a total discount of $8 divided by 2 items

Calculation:

Step 1 (Brackets): 5 × 9 - 8 ÷ 2

Step 2 (Multiplication): 45 - 8 ÷ 2

Step 3 (Division): 45 - 4

Step 4 (Subtraction): 41

Result: The total cost is $41.

Why This Calculation Matters

Practical Applications

Financial calculations with multiple operations
Engineering and scientific computations
Programming and algorithm development
Complex budgeting and expense tracking
Statistical analysis and data interpretation

Key Benefits

Ensures consistent and accurate calculations
Follows universally accepted mathematical standards
Helps avoid common calculation errors
Provides step-by-step breakdown for learning
Builds foundation for advanced mathematics

Common Mistakes & Tips

A common mistake is calculating from left to right without considering BODMAS rules. For example, in 2 + 3 × 4, the correct answer is 14 (not 20) because multiplication comes before addition. Always follow BODMAS rules regardless of the order in which operations appear.

Incorrect placement of parentheses can completely change the result. For example, 5 + 3 × 2 = 11, but (5 + 3) × 2 = 16. Always double-check your parentheses to ensure they group the operations as intended.

Division and multiplication have equal priority and are performed from left to right. In 12 ÷ 3 × 2, the correct answer is 8 (not 2), because we first divide 12 by 3 to get 4, then multiply by 2 to get 8.

Frequently Asked Questions

BODMAS and PEMDAS are the same order of operations with different terminology. BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is commonly used in the UK and some other countries, while PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is used in the US. Both represent the same mathematical rules.

When dealing with nested parentheses, always start with the innermost parentheses and work your way out. For example, in 3 × (4 + (5 - 2)), first calculate 5 - 2 = 3, then 4 + 3 = 7, and finally 3 × 7 = 21.

Roots and square roots fall under the "Orders" category in BODMAS, along with exponents. They are calculated after brackets but before division, multiplication, addition, and subtraction. For example, in 9 + √16 × 2, first calculate √16 = 4, then 4 × 2 = 8, and finally 9 + 8 = 17.

References & Disclaimer

Mathematical Disclaimer

This BODMAS calculator provides results based on standard mathematical rules. While we strive for accuracy, rounding may occur based on the decimal places selected. For critical calculations, please verify results independently and consult with appropriate professionals.

References

Math Is Fun: Order of Operations - Comprehensive guide to BODMAS rules with examples
Khan Academy: Order of Operations - Video tutorials on BODMAS principles
NRICH: BODMAS Explained - Mathematical explanation of order of operations

Accuracy Notice

This calculator performs calculations to the precision selected by the user. Results may be rounded and should not be considered exact for applications requiring high precision. For scientific, engineering, or financial applications requiring exact calculations, please verify results independently.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

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