Scientific Calculator

The order of operations, and the two conventions people argue about

Expressions are worked in the standard order: brackets first, then factorials and percentages, then powers, then signs and roots, then multiplication and division, then addition and subtraction. Powers stack from the right, so 2^3^2 is 2^9 = 512, not 8² = 64 — the same rule mathematics uses for a tower of exponents.

The first convention worth knowing is that the minus sign in front of a power is applied after it: −2² is −(2²) = −4. That is how algebra reads −x², and it is what Casio and Texas Instruments calculators and languages such as Python do. Spreadsheets are the well-known exception — in Excel and Google Sheets =-2^2 gives 4, because they apply the sign first. To square a negative number here, bracket it: (−2)² = 4. The “Read as” line shows −(2^2), so the reading is never a surprise.

The second is implicit multiplication — 2π, 3(4+5), 2sin(30). It binds tighter than an explicit ÷, so 1/2π means 1/(2π) = 0.159…, as anyone writing 1/2πf intends, and the viral 6÷2(1+2) equals 1, as on Casio's fx models. Strictly left-to-right calculators such as the TI-84 give 9; write the sign — 6÷2×(1+2) — and this one gives 9 too. A number straight after another operand, as in “2 3”, is reported as a typing mistake, never guessed at.

Degrees, radians and the trigonometric keys

Trigonometric functions depend on the angle unit, and the wrong unit is the most common reason a calculator answer disagrees with a textbook. In degree mode sin(30) is 0.5; in radian mode the same keystrokes give −0.988, because 30 radians is nearly five full turns. A full turn is 360° or 2π radians, so 180° = π and 1 radian ≈ 57.30°. The current unit is printed at the top of the display.

Inverse functions — sin⁻¹, cos⁻¹, tan⁻¹ — return an angle in the selected unit: sin⁻¹(0.5) is 30 in degrees and 0.5236 (π/6) in radians, and asin(2) is reported as needing a value from −1 to 1. Hyperbolic functions (sinh, cosh, tanh and their inverses) ignore the angle setting.

At the standard angles the results are exact: sin 30° is 0.5, cos 90° is 0, and tan 90° is reported as undefined. Software calculators often show tan 90° as an enormous number such as 1.6 × 10¹⁶, and sin(π) as 1.2 × 10⁻¹⁶ rather than 0 — artefacts of π not being exactly representable in binary. Both are cleaned up here.

Logarithms, roots, factorials and combinations

log is base 10, ln is the natural logarithm (base e ≈ 2.71828) and log₂ is base 2. Any other base takes a second argument, log(x, base): log(8, 2) = 3 — the change-of-base rule, log_b x = ln x ÷ ln b, done for you. eˣ and 10ˣ have their own keys.

√ and ∛ take square and cube roots, and root(x, n) takes any root: root(27, 3) = 3. A negative number has a real root only when the index is odd, so ∛−8 = −2 and root(−32, 5) = −2, while √−4 is reported as a domain error. This calculator works in real numbers; it does not return complex results.

n! is the factorial for whole numbers from 0 to 170; 171! exceeds the largest double-precision number, about 1.8 × 10³⁰⁸, and is reported as an overflow. nCr(n, r) counts combinations and nPr(n, r) arrangements: nCr(52, 5) = 2,598,960 poker hands, nPr(10, 3) = 720 podium finishes from ten runners. Both are computed exactly before the final rounding.

The % key divides by 100 and nothing more: 200 × 15% is 30, but 200 + 15% is 200.15, not 230. Desk calculators that apply a hidden add-on rule are how wrong invoices happen; the percentage calculator states each formula instead. For remainders, type mod(a, b): mod(17, 5) = 2.

Precision, display and why 0.1 + 0.2 shows 0.3

Arithmetic is IEEE 754 double precision, good to about 15–16 significant digits, and results are displayed to 12. The gap is deliberate: 0.1 has no exact binary form, so 0.1 + 0.2 is stored as 0.30000000000000004, and rounding to 12 digits shows the true answer, 0.3. A sum that cancels to within 10⁻¹⁴ of its inputs, such as 0.1 + 0.2 − 0.3, is exactly zero rather than 5.55 × 10⁻¹⁷.

Results of a trillion or more, or below one millionth, switch to scientific notation, shown as 6.02 × 10²³. To type one, use the EXP key or a capital E: 6.02E23, 1.5E-7. A lowercase e is always Euler's number, so 2e3 is rejected with a hint rather than silently computed as 2 × e × 3 = 16.3 when you meant 2,000.

Errors are named — division by zero, mismatched parentheses, √ of a negative number — rather than shown as NaN. What this calculator does not do is algebra, complex numbers or exact fractions; the fraction calculator keeps results as exact numerators and denominators, and the statistics tools handle lists of numbers.

Ans, memory and history

Every result becomes Ans. After =, the expression stays on screen so you can check it; an operator next continues from the answer (Ans×2), while a digit starts afresh. Click into the display to edit the expression and press = again. M+ and M− add the current result to memory or take it away, MR inserts M, and MC clears it.

History keeps your last 50 calculations for this visit: select an expression to edit it, or a result to insert it, or step through with the ↑ and ↓ keys. Nothing is stored or sent — the expression is parsed by the page's own code, and the calculator keeps working with the network switched off.