Arithmetic Operations Calculator
Evaluate Arithmetic Expressions using Order Of Operations rules with PEMDAS or BODMAS
You can enter a valid Arithmetic expression in the text box below and get the result instantly. The processing is done locally
Valid operators are +, -, *, /, ^, % , (), [], {}
What is a Math Expression?
- A Math expression is a combination of numbers, variables and operators.
- The operators are in between the numbers and this is referred to as infix notation.
- An expression has at least a minimum of 2 numbers and an operator.
1 * 2 is an expression - Math expressions can be classified into Arithmetic Expressions and Algebraic Expression.
- Arithmetic Expression contains only numbers and operators
3 + 4
5 - 6 + 9 * 10
(8/4) * (7/3)
- Algebraic Expressions contain numbers with variables and operators.
2x + 3
5a + 3b + 20
Addition (+)
Subtraction (-)
Multiplication (*)
Division (/)
Exponents (^)
Modulo (%)
Square root ()
with Use of (), [], {}
How to Use the Arithmetic Expressions Calculator?
- In the text box labelled as 'Expression', you can copy paste your expression or type in a valid expression using the keypad.
- The result of the expression is automatically computed and shown in the output box instantly.
- You can enter numbers (decimal, real number, fraction).
- You can Use the following operators. Operators should be between the numbers except that of unary operators are supported +, - , / ,÷, * , x , %,^
You can enter * or x for multiplication and / or ÷ for division - These expressions are also supported where there is no operator between number and parentheses. It is taken as multiplication for eg -2(3) is taken as -2 * (3)
- You can use any of the parenthese - flower bracket, round bracket or square bracket - (), {}, [] each opening parentheses or bracket must have a proper closing bracket
- If an invalid expression is entered, the output shows blank
The Order of Operations Rules
Examples of Arithmetic Expressions
- (2 + 3) * 4 - 5
- 2 ^ 3 + 4 * 5 - 6
- 2 / (3 + 4) * 5 – 6
- (10 - 5) / 2 + 1
- 2 + 3 * 4 / 5 - 6
The expressions are written in infix notation, which is the most common way to write arithmetic expressions. In infix notation, the operators are written between the operands
- Parentheses ( )
- Exponents (^)
- Multiplication (*)
- Division (/)
- Addition (+)
- Subtraction (-)
- Evaluate all expressions inside parentheses first.
- Evaluate all exponents next.
- Evaluate multiplication and division from left to right.
- Evaluate addition and subtraction from left to right.
If there are multiple operators of the same precedence, they are evaluated from left to right.
For example, to evaluate the expression (10 - 5) / 2 + 1,
- First evaluate the expression inside the parentheses, which is 10 - 5 = 5.
- Then, divide 5 by 2, which gives 2.5.
- Finally, add 1 to 2.5, which gives the final answer of 3.5.
Valid operators for order of operations:
The order of operation rules are as follows:
PEMDAS vs BODMAS
BODMAS and PEMDAS are two different acronyms for the same order of operations rules
BODMAS: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Both PEMDAS and BODMAS are widely used in mathematics education and in many scientific and engineering fields. They are important to ensure standardization in calculations so everyone gets a the same correct answer with the same expression
The only difference between the two acronyms is the word used for exponents. In the UK, exponents are called orders, while in the US, they are called exponents. So both BODMAS and PEMDAS are the same
See example below on how to use the BODMAS/PEMDAS rules to evaluate an expression: (2 + 3) * 4 - 5
- Evaluate the expression inside the parentheses first: 2 + 3 = 5.
- Multiply 5 * 4 = 20.
- Subtract 5 from 20: 20 - 5 = 15.
- Therefore, the final answer is 15.
The order of operations can be used to create expressions that have different values depending on which operations are performed first. For example, the expression 2 * 3 + 4 can have the value of 10 or 22, depending on whether you multiply 2 * 3 or add 2 + 4 first.
The order of operations can be used to create puzzles and challenges. This puzzle is a commonly posed challenge : 8 / 2 * (2+2)
- The answer is 16 or 1? Try it out with the expression solver above!
The order of operations is not universal. There are some variations in the order of operations that are used in different countries and in different fields of mathematics.
There are other order of operations besides BODMAS and PEMDAS.
- One example is the Reverse Polish Notation (RPN) order of operations. In RPN, the operands are written before the operators. For example, the expression 2 + 3 would be written as 2 3 + in RPN.
- Another example is the Polish Notation (PN) order of operations. In PN, the operators are written before the operands. For example, the expression 2 + 3 would be written as + 2 3 in PN.
- RPN and PN are often used in computer programming, but they are not as commonly adopted as compared to BODMAS and PEMDAS.
The acronyms stand for:
Example of math calculations using the PEMDAS rule
Expression: 7 / 7 * 5 - 6
Expression : 1 * 5 - 6
Experssion : 5 - 6
Example of math calculations using the BODMAS rule
Expression: 2 - 4 ^ 2 / 2 + 9 - 2 * 4 / 2
Expression : 2 - 16 / 2 + 9 - 2 * 4 / 2
16 / 2 = 8
Expression: 2 - 8 + 9 - 2 * 4 / 2
2 * 4 = 8
Expression : 2 - 8 + 9 - 8 / 2
8 / 2 = 4
Expression: 2 - 8 + 9 - 4
2 - 8 = -6
Expression : -6 + 9 -4
-6 + 9 = 3
Expression: 3 - 4 = -1
Frequently Asked Questions on Arithmetic Operations Calculator
BODMAS is a rule for simplification of Arithmetic expression.
BODMAS stands for 'Brackets Orders Division Multiplication Addition and Subtraction.
Consider an example to evaluate using BODMAS : 2 + 5 * (4 - 3) ^ 2
Evaluate Brackets first (4-3) = 1
Then Orders = (1)^ 2 = 1
Then multiplication 2 + 5 * 1 = 5
Then addition 2 + 5 = 7
Result = 7
PEMDAS is a rule for simplification of Arithmetic expression.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Multiplication/Division is evaluated equally based on whichever comes first from left to right.
Addition / Subtraction is evaluated equally based on whichever comes first from left to right.
Yes, this calculator can handle complex Arithmetic expression but does not evaluate Algebraic expression whether simple or complex.
By complex Arithmetic expression we mean usage of many numbers and different operators with use of parentheses and exponents in different combinations
They are different acronymns used for the same order of rules expressions and they are all similar.
PEDMAS - Parantheses, Exponent, Division & Multiplication, Addition & Subtraction.
Whether it is Division First or Multiplication, they are of the same priority and evaluated from Left to Right.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition , Subtraction Instead of 'Orders' it is Exponents here.
They are identical GEMDAS - Grouping, Exponents, Multiplication, Division, Addition, Subtraction Instead of Parentheses and Brackets, the term 'Groupinp' is used.
MDAS - Multiplication, Division, Addition and Subtraction.
It is a subset of the above acronyms.
An Expression is a combination of numbers, variables with operator.
Example :
2 * 3 + 5
-5 -2 - 7
10x + 10x
An Equation has 2 expression statements separated by an = sign.
Example:
2x + 3 = 5
5 + 2 = 1 + 7
An expression is evaluated or simplified.
2 * 3 + 5 = 11
An Equation is usually solved
2x + 3 = 5 leads to x = 1
Both PEMDAS and BODMAS evaluate Left to Right after evaluating terms within parentheses first and Orders/Exponents.
Consider expression: 16 / 4 / (1+1)
Step 1: Evaluate Parentheses (1+1) = 2
Expression becomes 16 / 4 / 2
Step2: Evaluate from left to right (division or multiplication) 16/4 = 4
Expression becomes 4 / 2
Step 3 : Evaluate 4 / 2 = 2
Result is 2
To solve Arithmetic Expressions, follow the order of operation rules.
The order of operation rules are as follows:
1. Evaluate all expressions inside parentheses first.
2. Evaluate all exponents next.
3. Evaluate multiplication and division from left to right. Whichever comes first (* or /) is evaluated first .
4. Evaluate addition and subtraction from left to right. Whichever comes first (+ or -) is evaluated first.
5. If there are multiple operators of the same precedence, they are evaluated from left to right.
