Scientific Calculator (Online, with Trig, Logs, Roots and Factorials)
Free online scientific calculator: type a full expression with + − × ÷, powers, roots, sin cos tan in degrees, radians or gradians, ln, log, nCr, gcd, π, e and factorials, and see the order-of-operations steps, the fraction and other forms of the answer.
How it works
Order of operations: ( ) → functions (sin, √, ln…) → factorial !, percent % and degree ° → powers ^ (right to left) → sign − → × ÷ mod and implied × (left to right) → + − (left to right)
The expression is read by a small parser built for this page (no code evaluation): it splits the text into numbers, operators, functions and constants, then applies the standard order of operations used by school and scientific calculators. Powers group from the right (2^3^2 = 2^9), a leading minus applies after the power (−2^2 = −4), and a number written next to a bracket, a function or π multiplies it (2π, 3(4+1)). The “Interpreted as” line rewrites your input with the grouping made explicit, and the steps list every operation in the order it was done, with your numbers. Trigonometric functions use the angle mode you pick — degrees, radians or gradians — and inverse functions return angles in the same unit; a ° after a number marks it as degrees in any mode. Beyond the usual keys you can use sec, csc, cot, inverse hyperbolic functions, logarithms to any base, nth roots, nCr and nPr, gcd and lcm, min, max, mean, floor, ceil and round. Separate several calculations with semicolons and store results by name (r = 4; pi r^2), or reuse the previous answer with ans. Results are rounded to 12 significant digits to hide binary floating-point noise, so 0.1 + 0.2 shows 0.3, and the answer is also shown as a fraction, in scientific and engineering notation and, for whole numbers, in binary, octal and hexadecimal.
Worked example
With the default (2 + 3) * 4^2 - sqrt(81) + sin(30) in degree mode: the bracket gives 2 + 3 = 5, the power 4^2 = 16, so 5 × 16 = 80; sqrt(81) = 9 and sin 30° = 0.5. Working left to right, 80 − 9 = 71 and 71 + 0.5 = 71.5, which is 143/2 as a fraction and 7.15 × 10^1 in scientific notation. Typing r = 3; pi r^2 stores 3 as r and returns the area of a circle of radius 3, 28.2743338823, and nCr(10, 3) gives the 120 ways to choose 3 items from 10.
Sources: NIST Digital Library of Mathematical Functions — elementary functions · Order of operations (Wikipedia)
Frequently asked questions
How do I type powers, roots and π?
Use ^ for powers (5^3 = 125), sqrt( ) for square roots, cbrt( ) for cube roots and root(x, n) for any other root, e.g. root(32, 5) = 2 — x^(1/n) works too, including odd roots of negative numbers like (−8)^(1/3) = −2. Type pi or π for 3.14159… and e for 2.71828…
Should I use degrees or radians?
Use degrees for everyday angles (a 30° roof pitch, triangle problems in school). Use radians for calculus and physics formulas. sin(30) is 0.5 in degree mode but −0.988 in radian mode, so check the setting first — the calculator adds a note when a common degree angle is used in radian mode. You can also type 30° to force degrees in any mode.
Why is −2^2 equal to −4 and not 4?
Exponents are applied before the sign, exactly as in algebra: −2^2 means −(2^2) = −4, and the “Interpreted as” line shows it that way. Write (−2)^2 to square the negative number and get 4.
What do log, ln and % do here?
log is the base-10 logarithm (log(1000) = 3), ln is the natural logarithm (ln(e) = 1), log2 is base 2 and log(x, b) uses any base, so log(81, 3) = 4. The % sign divides the number before it by 100, so 15% = 0.15 and 200 * 15% = 30.
Can I store a value or reuse the last answer?
Yes. Separate steps with semicolons and give a value a name with =, for example a = 5; b = 12; sqrt(a^2 + b^2) gives 13. ans always holds the answer of the previous step, so 25^2; ans − 100 gives 525. The table “Each step” lists every line and its value.
How do I calculate combinations and permutations?
Use nCr(n, r) for combinations and nPr(n, r) for permutations: nCr(52, 5) = 2,598,960 five-card poker hands, and nPr(10, 3) = 720 ordered podium finishes from 10 runners. Factorials use !, e.g. 6! = 720.
How large a factorial can it calculate?
Factorials work for whole numbers from 0 to 170 (170! ≈ 7.26 × 10^306); 171! exceeds the largest double-precision number. For exact huge integers use the big number calculator.
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This calculator is for educational purposes. Double-check important results before acting on them.