How to Solve Everyday Arithmetic Step by Step

Everyone can do arithmetic. Almost nobody can do arithmetic on a long expression without losing track of the brackets, which is why the answer you get by hand and the answer the calculator gives so often disagree.

What the Math Solver does

Evaluates a whole expression at once — brackets, powers, multiplication, division, addition and subtraction — with standard precedence.

Precedence is the entire point. 2 + 3 × 4 is 14, not 20, and a surprising number of spreadsheet errors trace back to somebody assuming otherwise.

Open the Math Solver and follow the settings and checks below.

How it reads an expression

Setting	What it means
Order	Brackets, then powers, then × ÷, then + −, left to right within each level
Power symbol	^ — so 3 ^ 2 is nine
Brackets	Nest as deep as you like; every opening one needs a closing one
Implicit multiplication	Not assumed — write 2 × (3 + 1), not 2(3 + 1)
Decimals	Use a full stop, whatever your locale writes
Division by zero	Reported as an error rather than returned as infinity

How to use it

1. Type the whole expression on one line.
2. Use brackets wherever you are unsure — they cost nothing and remove all ambiguity.
3. Read the result. If it surprises you, the bracket placement is usually why.
4. Change one number and re-evaluate to see what drives the answer.

Practical advice

The single most common mistake in this kind of expression is the minus sign in front of a power. Written strictly, −3 ^ 2 evaluates as −(3 × 3) = −9, because the power binds tighter than the negation. If you meant the square of negative three, you have to write (−3) ^ 2, which gives 9. Spreadsheets differ from mathematical convention here, which is exactly why the two disagree with each other so often.

Common questions

Why is 2 + 3 × 4 fourteen and not twenty?

Because multiplication binds tighter than addition, so the expression is read as 2 + (3 × 4). This is the standard convention everywhere from school algebra to programming languages, and it is why writing the brackets you mean is worth the two extra keystrokes even when you are confident.

Can I write 2(3 + 1) without the multiplication sign?

No — implicit multiplication is not assumed, because it is genuinely ambiguous in longer expressions and different systems resolve it differently. Write 2 × (3 + 1). The strictness is deliberate: an expression that could be read two ways is worse than one that has to be typed out.

What does the ^ symbol do?

It raises to a power, so 3 ^ 2 is nine and 2 ^ 10 is 1,024. Note that it binds more tightly than a leading minus sign, so −3 ^ 2 gives −9 rather than 9. If you want the square of a negative number, put it in brackets.

Does it handle very large numbers exactly?

Up to a point. It uses standard double-precision floating point, which is exact for integers up to about 9 quadrillion and then starts rounding. It also inherits the familiar decimal artefacts — 0.1 + 0.2 lands just above 0.3 — which matter for money calculations and almost nowhere else.

Useful next tools

• Equation Solver — Solve linear and quadratic equations, with complex roots.
• Fraction Calculator — Add, subtract, multiply and divide fractions, simplified.
• Percentage Calculator — Percent of, is-what-percent, and percentage change.
• Unit Converter — Length, mass, temperature, area, volume, speed and data.
• Random Number Generator — Cryptographically random numbers in any range.
• CSV to Chart — Turn two columns into a bar or line chart.

Vootkit provides a browser calculator and educational guidance. Results depend on the values and units you enter, so verify important financial, academic, safety or professional decisions with an appropriate authoritative source.