# Scientific Calculator - Trig, Log, Exponents, and Parentheses Free online expression calculator with order of operations. Degrees by default. Runs privately in your browser. ### Expression Deg Rad Expression _sin(30)_ Display _0.5_ sin cos tan log ln C asin acos atan √ exp ⌫ π e n! abs ( ) 7 8 9 ÷ ^ % 4 5 6 × Ans ± 1 2 3 − 0 . + = Clear Copy Default Deg so sin(30) = 0.5. Keyboard: digits, operators, Enter, Escape, and Backspace. ### ResultCalculated Copy Expression sin(30) 0.5 Degrees · Ans = 0 ### What Is a Scientific Calculator and Why Do You Need One? A **scientific calculator** evaluates a full expression: parentheses, exponents, roots, logs, and trigonometric functions, with a defined order of operations. It is not a four-function desk machine that only keeps two registers. On a basic calculator, pressing 2 + 3 × 4 can equal 20 because multiply runs after you already added. On this page, **2 + 3 × 4 = 14**, because multiplication binds tighter than addition. The default example is the first identity students check: **sin(30) in degree mode equals 0.5**. If the Deg/Rad toggle is on radians, sin(30) is sine of 30 radians and is not 1/2. That single switch is the most common source of “the calculator is broken” reports in trigonometry. This **free online scientific calculator**calculates in your browser. After the page loads, it still works offline. Last expression, angle mode, and Ans are stored locally for up to 30 days. ### How to Use This Free Online Scientific Calculator 1. Leave **Deg** on for homework trig, or switch to **Rad** for calculus. 2. Type an expression or use the keypad. Functions insert with an opening parenthesis: `sin(`, `log(`, `sqrt(`. Close with `)`. 3. Press **=** (or Enter) to commit the result into **Ans**. The display also updates as soon as the expression is complete. 4. **C** clears the expression. Backspace deletes a character. **±** flips the sign of the last number. Copy the display when you need it on a worksheet. **Note:** this tool is for numerical results, not exact fractions or symbolic algebra. For sequential two-register arithmetic without PEMDAS, use the [basic calculator](https://www.toolcomb.com/basic-calculator). For a single logarithm in any base, see the [log calculator](https://www.toolcomb.com/log-calculator). For a^b with more explanation, see the [exponent calculator](https://www.toolcomb.com/exponent-calculator). ### Does It Use Order of Operations? (PEMDAS / Shunting-Yard) Yes. Parentheses first, then functions, then postfix `n!` and `%` (percent means ÷100), then exponents `^` (right-associative), then multiply and divide left to right, then add and subtract left to right. Unary minus is weaker than a power, so **−2^2 = −4** (that is −(2^2)), matching ordinary mathematical writing and Python’s `-2**2`. #### Worked expressions: - 2 + 3 × 4 = 14 - (2 + 3) × 4 = 20 - 2^3^2 = 2^(3^2) = 512, not (2^3)^2 = 64 - sin(30) = 0.5 in Deg - log(1000) = 3 (common log, base 10) - ln(e) = 1 - 5! = 120 - 50% = 0.5 Implicit multiplication is inserted between a value and a following value: `2π`, `2(3+4)`, `(2)(3)`, `2sin(30)`. Functions still require parentheses so `sin 30` is rejected instead of guessing. To square a negative, wrap it: `(-2)^2` = 4. A leading minus on an empty line starts a negative constant. Log of a power: log(2^10) is log(1024) ≈ 3.0103, not 10, because log is base 10. ln(e^5) displays as 5 after rounding. 10^log(7) should return 7 or a binary neighbor; display rounding often snaps it to 7, which is for reading, not a proof of exact inverses. Cube roots of negatives are not a dedicated key; `(-8)^(1/3)` may return an error rather than print −2. Use odd-root algebra on paper.`1/2π` is (1/2)×π here; write `1/(2π)` for the reciprocal of 2π. ### Degrees vs Radians - What Is sin(30) in Degrees? In **degree mode**, a full circle is 360°, and **sin(30) = 1/2 = 0.5**, cos(60) = 0.5, tan(45) = 1. Inverse trig returns degrees: asin(0.5) = 30. That is what high-school homework almost always wants, so this page defaults to Deg. In **radian mode**, a full circle is 2π. sin(π/6) = 0.5, and sin(30) is sine of 30 radians ≈ −0.988. Cosine and tangent follow the same unit. Calculus derivatives of sin and cos assume radians. If a physics formula uses ωt with t in seconds and ω in s⁻¹, those arguments are radians. There is no automatic unit conversion of a typed number unless you write it: to convert 30° to radians by hand, 30 × π/180. To convert π/6 rad to degrees, (π/6)×180/π = 30. The toggle only changes how sin, cos, tan, asin, acos, and atan interpret their argument or result. log, ln, sqrt, exp, abs, and ^ do not care about Deg/Rad. ### How to Enter Exponents, Logs, and Factorial Use **^** for powers: 2^8 = 256, 9^0.5 = 3 (same idea as sqrt(9)). e^x can be typed as `e^x` or `exp(x)`. Scientific literals such as `6.02e23` are numbers, not the constant e. The constant e is the key labeled e (Euler’s number). **log** is log₁₀. **ln** is the natural log. log(100) = 2, ln(1) = 0. Both reject zero and negatives. For an arbitrary base, change-of-base is log(x)/ log(b) (or ln), or use the dedicated [log calculator](https://www.toolcomb.com/log-calculator). **n!** is integer factorial from 0 through 170. 0! = 1, 5! = 120, 10! = 3,628,800. Values above 170 are rejected. Non-integers and negatives are also rejected. Quadratic equations belong on the [quadratic formula calculator](https://www.toolcomb.com/quadratic-formula-calculator). You can still type the discriminant by hand here as `sqrt(b^2-4*a*c)` with numbers filled in, but that is not a symbolic solver. ### Functions, Constants, and Domain Errors | Key | Meaning | Rejected when | | --- | --- | --- | | sin cos tan | Trig; Deg or Rad | tan at odd multiples of 90° (cos ≈ 0) | | asin acos atan | Inverse trig; result in Deg or Rad | asin/acos outside [−1, 1] | | log ln | log₁₀ and ln | argument ≤ 0 | | sqrt exp abs | √x, e^x, \|x\| | sqrt of a negative | | π e Ans | pi, Euler’s number, last result | - | | n! % | integer factorial; ÷100 | n not in 0..170 integers | | ÷ | Division | divide by 0 | % is postfix percent, not remainder (modulo). 200+10% is 200 + 0.1 = 200.1, not “increase 200 by 10%.” For that wording, use the percentage calculator’s increase mode. This keypad % matches expression parsers, not cash-register %. ### Numerical Precision and Supported Results Displayed values are rounded for readability. For example, sin(30°) displays as 0.5. Values very close to a boundary can be affected by normal numerical rounding, so check the domain and angle mode before using a result in a report. It will not simplify √8 to 2√2, keep 1/3 as a fraction, or solve for x. Exact rational arithmetic belongs on a fraction tool. Huge factorials stop at 170!. Powers that overflow print an error instead of Infinity. Complex results (sqrt(−1), log(−2)) are errors, not i. Display rounding to twelve significant digits (and snapping values extremely close to integers) is why sin(30) reads 0.5 instead of 0.49999999999999994. Cos(90) may read 0 even though the internal cosine of 90×π/180 is a tiny residue; tan(90) is still blocked when that cosine is near zero. Copying more digits than your data had is a reporting mistake, not extra precision the calculator invented. ### Where a Scientific Calculator Shows Up in Real Work #### 1. Trigonometry homework Right-triangle ratios, unit-circle values, and inverse trig to find an angle. Check Deg first. sin(30)=0.5, cos(30)=√3/2 ≈ 0.866025403784, tan(30)=1/√3 ≈ 0.577. #### 2. Chemistry pH and logs pH = −log([H+]). Type `-log(1e-7)` for 7. Absorbance and first-order decay also live in log/ln space. The dedicated log page is better when the base is not 10 or e. #### 3. Physics powers and roots Kinetic energy ½mv² is `0.5*m*v^2`. Period of a spring 2π√(m/k). Keep radians in mind if a formula already multiplied by π. #### 4. Statistics combinatorics n! for permutations. 10! / (3!×7!) for a combination - type it with parentheses. 170! is the hard cap. ### Common Scientific Calculator Mistakes Leaving the calculator in radians during degree homework. Writing sin30 without parentheses. Using log when the assignment meant ln (or the reverse). Treating 2^3^2 as 64. Using % as “add a tip.” Expecting exact 1/3. Comparing this page to a two-register [basic calculator](https://www.toolcomb.com/basic-calculator) and calling PEMDAS a bug. Inverse trig range: asin returns −90° to 90° (or −π/2 to π/2). acos returns 0 to 180° (or 0 to π). The other angle that also has that sine is your job via the unit circle, not this display. tan(90°) is undefined, not “a huge number.” Chain calculations with Ans instead of retyping a long display. After sin(30) shows 0.5, press = to store Ans, then type `2*Ans` for 1. If you edit the expression to something incomplete, the live display waits; Equals will then show an incomplete-expression error rather than silently keeping the old number as if it were new. C clears the line, not Ans. There is no undo beyond Backspace. Hyperbolic functions (sinh, cosh), polar/rectangular conversions, numerical integrals, and matrix modes are not on this keypad. Complex numbers are not on this keypad. Sexagesimal degrees-minutes-seconds must be converted to decimal degrees first: 30°30′ is 30.5, not 30.30. Binary, hex, and programmer modes belong on other tools. Keep this page for numerical expressions with the functions listed above. Parentheses must match. `sin(30` is incomplete. Extra closing parens throw mismatched parentheses. A trailing operator `2+3+` is incomplete until you finish the term. Empty parentheses `sin()` fail as an incomplete or invalid argument. Those rules are stricter than a handheld that might wait on a blinking cursor, and that strictness keeps the calculator from guessing. ### Scientific vs Basic and Graphing Calculators A **basic calculator** is the two-register machine on this site: you press operations in sequence. A **scientific calculator** (this page) is an calculator with trig, logs, powers, and parentheses. A **graphing calculator** additionally plots y = f(x) and often stores lists; this page does not plot. This calculator reports numerical values, so √8 displays about 2.82842712475. Simplify symbolic forms by hand when your coursework requires them. Handheld scientifics differ in whether 1/2π is (1/2)π or 1/(2π). Here, implicit multiply is the same precedence as ×, so `1/2π` tokenizes as 1 / 2 × π, which is (1/2)×π, not 1/(2π). Write `1/(2π)` when that is what you mean. The same precedence trap exists on many physical calculators. Memory on a pocket scientific is often M+, MR, MC. Here the reusable slot is **Ans**: the last value committed with Equals, or the last successful evaluation stored after you press =. Type `Ans^2` to square it. Clearing the expression does not wipe Ans. There is no second independent memory register. ### Worked Physics and Chemistry Expressions Period of a 0.25 kg mass on a 100 N/m spring: T = 2π√(m/k). Type `2πsqrt(0.25/100)` in Deg or Rad - no trig is involved, so the toggle does not matter. √(0.0025) = 0.05, times 2π ≈ 0.314159 seconds. If you forget the closing parenthesis after 100, the calculator reports a mismatched-parentheses error instead of inventing a value. Horizontal range for a projectile (no air) R = v²sin(2θ)/g. With v = 20 m/s, θ = 30°, g = 9.81, Deg on:`20^2*sin(2*30)/9.81`. sin(60°) ≈ 0.866025, 400×0.866025/9.81 ≈ 35.3 m. If Rad is on, sin(60) is sine of 60 radians and the range is nonsense. Check the toggle before you blame g. pH of 2.5×10⁻⁴ M acid (strong, complete): `-log(2.5e-4)` ≈ 3.602. The unary minus applies to the log, not to the argument. `log(-2.5e-4)` is rejected (non-positive). First-order half-life estimates that use ln(2)/k are `ln(2)/k` with k in s⁻¹. Combinations: C(10,3) = 10! / (3!×7!). Type `10!/(3!*7!)` = 120. 171! will not run. Mixing factorial with a decimal `3.5!` is rejected. Nested factorials `(3!)!` = 720, which is 6!, not a special key. Keyboard when the expression field is not focused: digits,`.`, `+`, `-`, `*` or `x` for ×, `/` for ÷, `^`, `%`, parentheses, `!`, Enter for equals, Escape for clear, Backspace to delete. When the expression box is focused, type normally and use Enter to commit Ans. ### Frequently Asked Questions (FAQ) - Scientific Calculator #### What is the difference between a scientific calculator and a basic calculator? A basic calculator is two-register sequential arithmetic: 2 + 3 × 4 may equal 20 if multiply runs after you already added. This scientific calculator parses a full expression with parentheses, exponents, and functions, so 2 + 3 × 4 = 14. #### Should I use degrees or radians? Use degrees for most high-school trig (sin(30°) = 0.5). Use radians for calculus, the unit circle in higher math, and many physics formulas. This page defaults to degrees. Inverse trig returns an angle in the same unit as the toggle. #### How do I enter exponents? Use the ^ key: 2^8 is 256. For e to a power, use exp(x) or e^x. For scientific notation of a typed number, you can also write 6.02e23 as a literal. #### What is sin(30) in degrees? In degree mode, sin(30) = 0.5. In radian mode, sin(30) is sin of 30 radians, which is not 0.5. Always check the Deg/Rad toggle before you copy a trig result. #### Does this calculator use order of operations? Yes. It evaluates parentheses, functions, factorial and percent, powers, multiplication and division, then addition and subtraction. It is intended for numerical calculations, not exact fractional or symbolic algebra results. #### Does this scientific calculator upload my expressions? No. Evaluation runs in your browser with JavaScript. Nothing is sent to a server. After the page loads, the tool still works if the network drops. ### Why Choose Our Scientific Calculator? - **Free, no account.** Unlimited expressions. - **Private.** Calculations stay in the browser. - **Standard order of operations** for full expressions. - **Degrees by default** so sin(30) = 0.5. - **Honest domain errors** for ÷0, log of non-positives, sqrt of negatives, and asin outside [−1, 1]. - **Ans, keyboard, and local 30-day memory.** - **Works offline** after the first page load. ## Related Tools Discover more free tools that might help with your next task. [Area Calculator Calculate area of squares, rectangles, triangles, circles, and more Use Tool](https://www.toolcomb.com/area-calculator) [Average Calculator Calculate mean, median, mode, and range from a list of numbers Use Tool](https://www.toolcomb.com/average-calculator) [Basic Calculator Add, subtract, multiply, and divide with a free online calculator Use Tool](https://www.toolcomb.com/basic-calculator) [Big Number Calculator Add, subtract, multiply, and divide integers too large for a standard calculator Use Tool](https://www.toolcomb.com/big-number-calculator) [Binary Calculator Add, subtract, and convert binary numbers to decimal and hex Use Tool](https://www.toolcomb.com/binary-calculator) [Circle Calculator Find radius, diameter, circumference, area, arc length, and sector area Use Tool](https://www.toolcomb.com/circle-calculator) ### Related guides Read the how-to, then come back to this tool when you are ready to run it locally. - [Log Calculator: ln, log10, and Change of Base Evaluate natural log, base-10 log, and convert between bases with the change-of-base formula. A guide to log calculator natural log base 10 workflows.](https://www.toolcomb.com/blog/log-calculator-ln-log10-and-change-of-base) - [Matrix Calculator: 2×2 and 3×3 Limits, Determinant, and Inverse Add, multiply, find determinant and inverse for 2×2 and 3×3 matrices online. What matrix calculator online 2x2 3x3 pages can and cannot do.](https://www.toolcomb.com/blog/matrix-calculator-2x2-3x3-limits) - [Percentage Calculator: Three Kinds of Percent Problems Find percent of a number, what percent one number is of another, and find the whole from a part and percent. A guide to percentage calculator percent of workflows.](https://www.toolcomb.com/blog/percentage-calculator-three-kinds-of-percent-problems) [View All Tools](https://www.toolcomb.com/tools)