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Order of Operations Calculator (PEMDAS)

See why order matters: compute a + b × c the correct (PEMDAS) way versus naive left-to-right.

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Enter a, b, c and the Order of Operations Calculator (PEMDAS) works out Correct (PEMDAS): a + b × c, Naive left-to-right: (a + b) × c straight away. For instance, with a = 2, b = 3 and c = 4 it returns Correct (PEMDAS): a + b × c = 14 and Naive left-to-right: (a + b) × c = 20.

How to use it

  1. Enter your values: a, b, c.
  2. Read the result instantly: Correct (PEMDAS): a + b × c, Naive left-to-right: (a + b) × c.

Frequently asked questions

How does the Order of Operations Calculator (PEMDAS) work?

It takes a, b and c and derives Correct (PEMDAS): a + b × c and Naive left-to-right: (a + b) × c from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

3 values: a, b and c. Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With a = 2, b = 3 and c = 4, the calculator returns Correct (PEMDAS): a + b × c = 14 and Naive left-to-right: (a + b) × c = 20. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using a = 4, b = 6 and c = 8 instead, Correct (PEMDAS): a + b × c goes from 14 to 52 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to a = 1, b = 2 and c = 2, Correct (PEMDAS): a + b × c comes out at 5. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What is the difference between the Order of Operations Calculator (PEMDAS) and the First-Order ODE Solver?

This one returns Correct (PEMDAS): a + b × c and Naive left-to-right: (a + b) × c; the First-Order ODE Solver returns Result. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Group theory order calculator is the closest one after this: Analyse the classic finite groups — cyclic Zₙ, direct products Zₘ×Zₙ, dihedral Dₙ and symmetric Sₙ. It gives the group order, whether it is abelian, its structure, the number of generators for cyclic groups, and the order of any element you enter, including a permutation in cycle notation for Sₙ.

Where do the figures come from, and how current are they?

Base conversion and number-theory results are exact. Roman numerals follow the standard subtractive form used since the Middle Ages, which is not the only one the Romans themselves used.

Further reading

All guides →
ExplainerOrder of Operations (PEMDAS / BODMAS): Why the Order MattersPEMDAS and BODMAS are two names for one rule that fixes the order you evaluate a math expression — so everyone gets the same answer. Learn the rule with a worked example.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.