Type the exact same expression into two different calculators and you can genuinely get two different answers — not because either one is broken, but because of specific, well-defined rules about evaluation order that a lot of people never learned precisely.

PEMDAS, and Where It Actually Trips People Up

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right) — that's the standard order. The part people misremember most often: multiplication doesn't universally happen before division, and addition doesn't universally happen before subtraction. Within each of those pairs, you work strictly left to right. 10 − 3 + 2 is 9, not 5, because subtraction and addition share equal priority and are resolved left to right, not subtraction-first.

Why Exponents Evaluate Right to Left

Multiplication and addition are read left to right, but exponentiation is the odd one out — it's evaluated right to left. That means 2^3^2 isn't (2^3)^2 = 64; it's 2^(3^2) = 2^9 = 512. This right-associative rule is the actual mathematical convention (not a calculator quirk), and it's exactly why stacked exponents without explicit parentheses can look ambiguous even though there's only one mathematically correct reading.

Degrees vs. Radians: The Most Common Trig Mistake

sin(90) should equal 1 — but only if your calculator is in degree mode. In radian mode, the same input, 90, is interpreted as 90 radians (a huge angle, many full rotations around the circle), producing a completely different result. This single mode setting is responsible for more "my calculator is broken" confusion than almost anything else in trigonometry — always check which mode you're in before trusting a trig result that looks wrong.

Tip: If a trig result looks obviously wrong (like a sine or cosine value outside the -1 to 1 range, which is mathematically impossible for those two functions), the very first thing to check is whether you're in the wrong degree/radian mode — it's the single most common cause.

Why 0.1 + 0.2 Doesn't Always Equal 0.3

Computers store decimal numbers in binary, and just like 1/3 can't be written exactly as a finite decimal, many ordinary decimals like 0.1 can't be represented exactly in binary floating point. The stored value is an extremely close approximation, not the exact number — so adding two of these approximations together can produce a result like 0.30000000000000004 instead of a clean 0.3. This isn't a bug; it's an inherent, well-understood limitation of how floating-point numbers work in virtually every programming language and calculator, and well-built tools round the displayed result to hide it in ordinary use.

Try the Full Calculator

Build an expression with trig functions, logarithms, powers, and factorials — with correct operator precedence and a Deg/Rad toggle — using the free Scientific Calculator. No sign-up, and nothing you enter leaves your browser.

FAQ

Does this calculator respect the correct order of operations? Yes — it uses a proper expression parser (not a naive left-to-right evaluation), so multiplication and division happen before addition and subtraction, exponents are evaluated right-to-left as they should be, and parentheses always take priority.

Are the trig functions in degrees or radians? You can switch between them with the Deg/Rad toggle. In degree mode, sin(90) correctly returns 1; in radian mode, the same functions expect and interpret angles in radians instead.

Why does 2^3^2 equal 512 and not 64? Exponentiation is evaluated right to left, so 2^3^2 is actually 2^(3^2) = 2^9 = 512, not (2^3)^2 = 64 — this right-associative rule is the mathematical convention, even though it can look ambiguous written on one line without parentheses.

Is anything I calculate sent anywhere? No — every calculation is evaluated entirely in your browser using JavaScript, so nothing you enter is ever sent to a server.

Want to try trig, logs, and powers with correct precedence right now? Try the free Scientific Calculator — no sign-up.