The formula this page uses
Order of operations: ( ) → xⁿ → × and ÷ left to right → + and − left to right
Arithmetic Calculator
Solve arithmetic problems with clear steps, notation, and a final check. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Arithmetic Calculator explained
The short version
- Arithmetic has an order: brackets, then powers, then multiply and divide left to right, then add and subtract left to right.
- Multiply and divide have the same rank, so 48 ÷ 4 × 2 runs left to right and equals 24, not 6.
- A fraction, a decimal and a percent are three spellings of one number: 3/4 = 0.75 = 75%.
What each part means
SymbolWhat it means
( ) — BracketsAnything inside is finished first, working outward from the innermost pair.
xⁿ — Powers and rootsApplied after brackets. A minus sign in front is not part of the base unless brackets say so.
× ÷ — Multiply and divideEqual rank. Read them left to right like words on a page.
+ − — Add and subtractEqual rank, done last, also left to right.
Show your work: a full example
- Start with the expression8 + 3 × (10 − 6)² ÷ 4
- Brackets first10 − 6 = 4, so the expression is 8 + 3 × 4² ÷ 4
- Power next4² = 16, so the expression is 8 + 3 × 16 ÷ 4
- Multiply, moving left to right3 × 16 = 48, so the expression is 8 + 48 ÷ 4
- Divide, still left to right48 ÷ 4 = 12, so the expression is 8 + 12
- Add last8 + 12 = 20
A second, different case
- A different case: unlike denominators3/4 + 2/5
- Find a shared denominator4 × 5 = 20
- Rewrite both fractions over 203/4 = 15/20 and 2/5 = 8/20
- Add the numerators only15/20 + 8/20 = 23/20
- Write it as a mixed number23/20 = 1 and 3/20
- Divide to get the decimal23 ÷ 20 = 1.15
- Multiply by 100 for the percent1.15 × 100 = 115%
Copy-ready example
8 + 3 × (10 − 6)² ÷ 4
Start with the expression
Questions about the Arithmetic Calculator
Does PEMDAS mean multiplication always beats division?
No, and that is the most misread part of the mnemonic. Multiply and divide sit on the same rung, and so do add and subtract. Within a rung you work left to right, which is why 48 ÷ 4 × 2 is 24.
Why does 1/3 turn into 0.333… and never stop?
A decimal stops only when the denominator's prime factors are 2s and 5s, because our place values are tenths, hundredths and thousandths. 3 is neither, so the division never lands exactly and the digit repeats forever.
Is −3² equal to 9 or −9?
It is −9. The power sticks to the 3 only, so you square first and then apply the minus: −(3 × 3) = −9. You get +9 only when brackets make the minus part of the base, as in (−3)².
How do I add 2/5 to 0.7?
Move both into one form. 2/5 = 0.4, so 0.4 + 0.7 = 1.1. Going the other way works too: 0.7 = 7/10, and 4/10 + 7/10 = 11/10, which is the same 1.1.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
A calculator gives you the number. If you also want to be able to do this without one, order of operations walks through the method step by step, with a worked example and the mistakes that cost marks.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.