Order of Operations Calculator | PEMDAS Calculator

Order of Operations Calculator

To ensure accuracy in the calculation of mathematical operations, it is essential to follow a set of specific rules. These regulations establish the order of operations, facilitating the systematic and orderly resolution of mathematical expressions involving two or more operations. This approach allows breaking down the process step by step, ensuring proper and precise execution.

We present to you an excellent calculator for order of operations that will help you understand how to solve mathematical operations following the proper order of operations. This tool provides step-by-step solutions and the opportunity to visualize the process in a tree-like structure, revealing the order in which various operations have been resolved.

The order of operations calculator, also known as PEMDAS Calculator, automatically solves the expression as you input it. The syntax required for entering different operations is detailed in the following table, ensuring precise and efficient use of the tool.

Command Operators, Functions, and Constants
+ Addition
*, x Multiplication
/ Division
sqrt() Square Root
^ Raise to a Power
 pi π, (3.1416…)
log Logarithm Base 10
ln Natural Logarithm
e Base of Natural Logarithm
abs() Absolute Value
sin, cos, tan, asin, acos, atan, sinh, cosh, tanh Trigonometric Operations
() Parentheses

What is the order of operations?

The order of operations refers to a set of standardized rules that dictate the sequence in which various operations, such as addition, subtraction, multiplication, and division, should be performed.

Adhering to the proper order of operations is crucial for simplifying and solving various algebraic problems. Failure to apply the correct order of operations may lead to different interpretations of a mathematical expression among different individuals, resulting in divergent solutions. Consequently, precise adherence to these rules becomes critical to ensure consistency and accuracy in mathematical calculations.

What is PEMDAS?

PEMDAS is an acronym that represents the order of operations in arithmetic and algebraic expressions. Each letter stands for a specific operation to be performed in a given order:

  1. P – Parentheses: Perform operations inside parentheses first.
  2. E – Exponents: Evaluate expressions with exponents or powers.
  3. M – Multiplication: Perform multiplication from left to right.
  4. D – Division: Perform division from left to right.
  5. A – Addition: Perform addition from left to right.
  6. S – Subtraction: Perform subtraction from left to right.

Following the PEMDAS order ensures a consistent and unambiguous way to evaluate mathematical expressions and equations.


Below, we provide some examples of solving mathematical operations by applying the appropriate order of operations:

Example 01: Order of operations with exponents 

Order of operations with exponents

In this example, we see how operations inside the parentheses are solved first, starting with the division of 9 by 3, and then proceeding with the addition operation. Subsequently, the result of the addition is squared. With the assistance of our calculator, we can better visualize the order of operations followed.

Example order of operations

Example 02: Order of operations with fractions

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