Order of Operations Calculator

The order of operations is the agreed sequence for evaluating an expression with more than one operator. Grouping symbols come first, then exponents and roots, then multiplication and division, and finally addition and subtraction. Without this shared rule, the same line of numbers could produce several different answers. It is a convention rather than a law of nature, but every textbook and programming language relies on it.

Two details cause most confusion. Multiplication and division have equal rank, so they are done from left to right as they appear. Addition and subtraction also share a rank and follow the same left to right rule. The acronym PEMDAS lists M before D only because a word needs an order, not because multiplication wins.

Type or paste an expression such as 2 × [5 + (3 - 1)^2] and press Calculate. You can use the keypad or your keyboard, with * or × for multiplication and / or ÷ for division. Square brackets and braces work exactly like parentheses, as long as each one closes with its matching partner. Spaces are optional, so 2*(3+4) and 2 × (3 + 4) give the same result.

Show Steps displays the full expression after each operation, with the part that changed highlighted. Use the PEMDAS and BODMAS switch to label the steps in the style your class uses. The Implied multiplication first setting is off by default and changes how expressions like 2(3) behave next to a division. The final answer appears above the steps and can be copied with one click.

The calculator always starts with the innermost group of brackets and works outward. Inside each group it applies exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Once a group is reduced to a single number, its brackets disappear and the next level is solved. The final answer is what remains when no operators are left.

Two rules trip people up more than any others. Stacked exponents group from the right, so 2^3^2 means 2^(3^2), which is 512. A minus sign in front of a power is applied after the power, so -3^2 is -9 while (-3)^2 is 9. The steps panel names each of these rules, including the left-to-right associativity that breaks ties within a shared rank.

These examples start with the classic traps and build up to nested brackets and real-world totals. Each one shows the input, the correct result and the rule that decides it. The later ones mirror homework problems and everyday bills.

Paste any of them into the tool above with Show Steps turned on. Comparing the rewritten lines with each explanation is the fastest way to lock the rules into memory.

Programming languages encode the order of operations as operator precedence and associativity. JavaScript and Python both group from the right, so 2 3 2 is 512 in each. They disagree on a leading minus: Python returns -4 for -2 2, while JavaScript refuses to run it at all. The language designers made that choice so nobody could misread the expression.

Spreadsheets add their own twist. In Microsoft Excel, =-2^2 returns 4 because negation is applied before the power. Excel also returns 64 for =2^3^2, because it reads exponents from the left. When results from code, a spreadsheet and a textbook disagree, add brackets until the intent is unambiguous.

// Exponents group from the right
console.log(2 ** 3 ** 2);   // 512, read as 2 ** (3 ** 2)
console.log((2 ** 3) ** 2); // 64

// A leading minus before ** is a syntax error in JavaScript
// console.log(-2 ** 2);    // SyntaxError
console.log((-2) ** 2);     // 4
console.log(-(2 ** 2));     // -4

print(2 ** 3 ** 2)    # 512, exponents group from the right
print(-2 ** 2)        # -4, the power is applied before the minus
print((-2) ** 2)      # 4
print(20 / 4 * 5)     # 25.0, division and multiplication run left to right
print(6 / 2 * (1 + 2))  # 9.0, no special rule for implied multiplication

Each step is computed with exact decimal arithmetic. A line like 0.1 + 0.2 shows 0.3, never a long tail of stray digits. Results that do not end, such as 10 ÷ 3, are rounded to 12 significant digits only when displayed. The unrounded value is carried into the next step, so rounding never compounds across a long expression.

Your expressions are evaluated inside your browser and are never uploaded, stored on a server or shared. The page does not need an account and works the same in every language version. It uses the same engine as the site's expression calculator, with extra support for square brackets, braces and labeled steps.

Most wrong answers come from treating PEMDAS as six separate ranks instead of four. The table below lists the mistakes teachers see most, along with the messages this tool shows for input it cannot read. Every fix can be checked by entering the expression above. Most of them disappear once you think in four ranks rather than six letters.

Bracket errors are the next most common problem, especially when square brackets and braces are mixed. Each opening symbol must close with the same kind of symbol, in reverse order. The tool points to the exact position of the first mismatch, so you can correct it quickly. More tools that follow the same rules are listed on the math calculators page.

The acronyms differ by country, but they describe the same rules and always produce the same answer. PEMDAS is common in the United States, BODMAS in India, Pakistan and much of Africa, and BIDMAS in the United Kingdom. GEMDAS replaces parentheses with grouping symbols to include brackets, braces and fraction bars. The middle letters change order in some versions, which is why the left to right rule matters.

Whichever acronym you learned, this order of operations calculator applies the same underlying ranks. Switching the label between PEMDAS and BODMAS changes only the names in the steps panel, never the result. Use the table below to translate between the systems. For trigonometry or logarithms inside an expression, switch to the scientific calculator.