Math · Arithmetic
Order of operations calculator.
Type an expression and watch it simplified one operation at a time: brackets, then exponents, then multiplication and division, then addition and subtraction.
Inputs
Answer and steps
Type an expression.
The order of operations
Do brackets first, then exponents (powers and roots), then multiplication and division, then addition and subtraction. Multiplication and division rank equally, so work left to right; addition and subtraction also rank equally and go left to right. Depending on where you learned it, this is called BODMAS, PEMDAS or GEMS. BEDMAS is the same order with Exponents in place of Orders.
Worked example. 7 + (6 × 5² + 3). Inside the brackets, the exponent comes first (5² = 25), then 6 × 25 = 150, then 150 + 3 = 153. Then 7 + 153 = 160.
Why the order matters. 3 + 6 × 2 is 15, because 6 × 2 = 12 comes first, while (3 + 6) × 2 is 18. And 12 ÷ 6 × 3 ÷ 2 works left to right: 12 ÷ 6 = 2, 2 × 3 = 6, 6 ÷ 2 = 3.
Stacked exponents. Exponents go top-down, so 4^3^2 means 4^(3^2) = 4^9 = 262144, not (4^3)^2.
To avoid ambiguity this tool does not accept a minus sign in front of brackets, a negative number directly before a power, or implied multiplication such as 2(3 + 4). Write 0 - (...) or (-2)^2 so the meaning is explicit.
Frequently asked questions
What is the order of operations?
Brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
What is the difference between PEMDAS, BODMAS and BEDMAS?
They are memory aids for the same order. PEMDAS says Parentheses and Exponents, BODMAS says Brackets and Orders, and BEDMAS says Brackets and Exponents.
Do multiplication and division come first or left to right?
They rank equally, so you go left to right. 12 ÷ 6 × 3 ÷ 2 is 3, Doing the multiplication first (6 × 3 = 18) would wrongly give 12 ÷ 18 ÷ 2 = 0.3333.
What is 3 + 6 × 2?
Multiplication comes before addition: 6 × 2 = 12, then 3 + 12 = 15. With brackets, (3 + 6) × 2 = 18.
How does the calculator treat 4^3^2?
Exponents are worked from the top down, so it is 4 to the power of (3^2) = 4^9 = 262144.
Sources
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For learning
Numbers are limited to about 15 digits and 120 characters per expression. Results are rounded for display. Check with your teacher's required method when you hand in homework.