Mathematical tables: operations precedence
Table shows order of common math operations, which should be applied while performing arithmetic calculations such as addition, subtraction, multilication, division etc.

Beta version#

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !

Order of operations#

Order (precedence)Operation nameOperation symbol
1curly bracketsShow source{}\{\}
2square bracketsShow source[][]
3curly bracketsShow source()()
3exponentiation and rootShow sourcexnxn\begin{aligned}x^n\\ \sqrt[n]{x}\end{aligned}
4multiplication and divisionShow sourcexyx÷yx/yx:yxy\begin{aligned}x \cdot y\\ x \div y\\ x/y\\ x:y \\ \frac{x}{y}\end{aligned}
5addition and subtractionShow sourcex+yxy\begin{aligned}x+y \\ x-y \end{aligned}

Some facts#

  • If arithmetic expression contains more than one operation (e.g. addition and multiplication), then in the general case we can get different results depending on applied operation order.
  • To solve this problem we should follow the common operation order rules was developed.
  • To get correct result, we should perform arithmetic operations in the following order:
    • operations in brackets - curly brackets first (the highest precedence), square brackets and finally expressions in round brackets (the lowest precedence),
      ⓘ Example: In the expression 2(3+4)2 \cdot \boxed{\left(3 + 4\right)} we should perform addition in brackets first, and the multiplication next.
    • exponentiation and root,
      ⓘ Example: In the expression 2342 \cdot \boxed{3^4} we should perform exponentiation first (raise three to power four), and perform multiplication next.
    • multiplication and division,
      ⓘ Example: In the expression 23+4\boxed{2 \cdot 3} + 4 we should perform multiplication first, and addition next.
    • addition and subtraction.
      ⓘ Example: In the expression 23+42 - 3 + 4 the order of operations doesn't matter, we can perform addition first, and subtraction next or vice versa. The addition and subtraction have the same precedence.
  • If you want to know more about properties of various math operations check out our other table: Number operations.

Tags and links to this website#

What tags this calculator has#

Permalink#

This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

Links to external sites (leaving Calculla?)#

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.
Please enable JavaScript.