Scientific Calculator

What this scientific calculator does

This is a practical, button-driven scientific calculator for numeric math. It handles the operators and functions you reach for in algebra, trigonometry, and pre-calculus: arithmetic, parentheses, powers, square roots, logarithms, trig functions and their inverses, factorial, and the constants π and e. Everything runs in your browser; nothing is sent anywhere.

Supported functions

• Arithmetic: + − × ÷ and parentheses ( ).
• Powers and roots: x² (square), xʸ (general power via ^), 10ˣ (insert 10^), eˣ (insert exp(), and √ (square root via sqrt().
• Trigonometric: sin, cos, tan and their inverses asin, acos, atan. These respect the angle mode toggle.
• Logarithmic: log (common log, base 10) and ln (natural log, base e).
• Other: n! (factorial, whole numbers from 0 through 170), π (pi), and e (Euler's number).

Degrees vs radians

Trig functions interpret their arguments differently depending on the angle mode:

• Degrees: a full circle is 360°. sin(30) = 0.5 and cos(60) = 0.5. This is the standard mode for most introductory algebra and trig classes.
• Radians: a full circle is 2π radians, which is roughly 6.283. In radian mode, sin(π/2) = 1 and cos(π) = −1. Radians are the standard in calculus and physics because derivative and integral formulas come out cleanly.

The inverse functions (asin, acos, atan) return their answers in whichever mode is active. So in degree mode, asin(0.5) = 30; in radian mode it returns about 0.524. Check the toggle at the top of the calculator if a trig answer looks wrong.

How the parser works

The calculator tokenizes your expression into numbers, operators, functions, parentheses, and constants. It uses the shunting-yard algorithm to convert the infix expression to a postfix (reverse Polish) representation, then walks that representation to compute the result. Each function call validates its own domain (no negative square roots, no log of non-positives, no asin or acos outside [-1, 1], no factorial of a non-integer or a value above 170).

The parser is local and only knows about the operators and functions listed in the supported functions section above. There is no symbolic algebra, no equation solver, and no graphing. For deeper explanations of specific topics, see the linked calculators below.

Order of operations, as this calculator implements it

The evaluation order follows the standard precedence ladder: parentheses and function calls first, then factorial, then exponents, then a leading minus, then multiplication and division left to right, then addition and subtraction left to right. Every claim below was probed against the engine, and each line shows the expression exactly as entered with the result the calculator actually returns:

• 2 + 3 * 4 = 14, not 20: multiplication before addition.
• 2^3^2 = 512: stacked exponents evaluate right to left, as 2^(3^2). With parentheses, (2^3)^2 = 64.
• -2^2 = -4: the exponent binds tighter than a leading minus, so it reads as -(2^2). (-2)^2 = 4.
• 2(3+4) = 14: implicit multiplication works before a parenthesis, and 2π works the same way.
• 3!^2 = 36: the factorial applies before the exponent, so it reads as (3!)^2.

All of this matches textbook PEMDAS with the two refinements textbooks usually leave implicit: exponent towers are right-associative, and a leading minus is applied after the exponent. Where a result surprises you, parentheses always win: they override every rule above.

Edge cases

• Division by zero. 1/0 returns the named error “Division by zero.” rather than Infinity. An infinite answer is almost never what a calculation meant, so the calculator flags it instead of continuing. 0/0 gets the same treatment.
• Floating-point display. Internally 0.1 + 0.2 is 0.30000000000000004, because 0.1 has no exact binary representation. The display rounds to ten decimal places, so you see 0.3. Enter 0.1 + 0.2 - 0.3 and the rounding can no longer hide it: the calculator shows 5.55111512 × 10^-17. That is IEEE 754 double precision working as designed, not a defect in this tool.
• Scientific-notation switch. Results at or above 10^12, or below 10^-6 in magnitude, display in scientific notation with eight decimal places; everything else shows up to ten decimal places.
• tan(90) in degrees is not an error. The engine converts degrees to radians before computing, and 90 degrees converts to a number that is close to but not exactly π/2. The tangent of that nearby angle is the enormous but finite 1.63312394 × 10^+16, and that is what you get.
• Factorial limits. Factorial accepts whole numbers from 0 to 170 only. 170! displays as 7.25741562 × 10^+306, the largest factorial a double can hold; 171! reports “Factorial too large (max 170)” and 3.5! is rejected because the engine implements integer factorial, not the gamma function.
• Domain guards. log and ln require positive inputs, sqrt requires a non-negative input, and asin and acos require values between -1 and 1. Each failure names itself in the error line under the display rather than returning NaN.

Working it out by hand

Take 2 + 3 * 4^2 - 6/3 and apply the ladder above one rung at a time:

1. Exponents first: 4^2 = 16, leaving 2 + 3 * 16 - 6/3.
2. Multiplication and division, left to right: 3 * 16 = 48 and 6/3 = 2, leaving 2 + 48 - 2.
3. Addition and subtraction, left to right: 2 + 48 - 2 = 48.

Result: 48, which is exactly what the calculator returns for this expression.

The common by-hand mistake is working strictly left to right, which gives 2 + 3 = 5, then 5 * 16 = 80 before the subtraction. The calculator never makes that mistake, and you can use the parenthesised form (2+3) * 4^2 = 80 to see what the wrong reading would have produced.

What this calculator does not do

• No graphing. The calculator produces a numeric answer; it does not plot equations or produce a chart.
• No symbolic algebra. It evaluates numbers, not expressions in terms of variables. There is no x to solve for.
• No CAS. A computer algebra system can simplify, factor, and rearrange symbolic expressions. This calculator only computes numerical values.
• No equation solver. For ax² + bx + c = 0 problems, use the quadratic formula calculator.

For focused explanations of single topics, the dedicated calculators are usually a better fit:

• Exponent calculator for powers, with step-by-step explanations of negative and fractional exponents.
• Log calculator for logarithms in any base, with the change-of-base formula explained.
• Square root calculator for the simplified radical form and the perfect square check.
• Percentage calculator for the three standard percent questions.
• Factor calculator for prime factorization, factor pairs, and GCF.

Worked examples

• sin(30) in degree mode = 0.5.
• cos(π) in radian mode = −1.
• log(1000) = 3.
• ln(e) = 1.
• 2^10 = 1,024.
• sqrt(2) ≈ 1.4142.
• 5! = 120.
• 2π + sin(90) in degree mode ≈ 7.283.

Common mistakes

• Wrong angle mode. If a trig answer looks completely off, switch between Deg and Rad first; that fixes most surprises.
• Confusing log with ln. The button labeled log is base 10; ln is natural log (base e). The log calculator explains the distinction in detail.
• Mismatched parentheses. The error message at the bottom of the display points out the problem. Use the ( and ) buttons to balance.
• Taking a square root or log of a negative or zero value. Those operations are undefined in the real numbers; the calculator flags them rather than returning NaN.
• Factorials over 170. The result would overflow floating-point precision, so the calculator caps the factorial domain.

Your calculations stay in the page

Every expression you build is evaluated by this page in your browser. What you type is not sent to a server and not stored after you close the tab, and the recent-expressions list lives only in the page while it is open. There is no account and nothing to sign up for.

Sources

• IEEE 754-2019, IEEE Standard for Floating-Point Arithmetic for the double-precision number format every result here is computed in, including why 0.1 has no exact binary representation and what the rounding rules are.

Rounding the display to ten decimal places and switching to scientific notation outside the 10^-6 to 10^12 range are this site’s own display conventions, chosen for readability. The underlying arithmetic is unrounded IEEE 754 double precision throughout.

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