Scientific Calculator
Trigonometry, logarithms, exponents, factorial and constants — free, instant, no signup
What is this Scientific Calculator?
This free online scientific calculator provides the complete set of mathematical functions needed for Class 10, 11, and 12 board exams, JEE Main and Advanced, NEET, engineering coursework, and everyday scientific calculations — all in your browser, with no app install or sign-up required. It handles trigonometry (sin, cos, tan and their inverses), logarithms (natural log ln and base-10 log), exponents (x^y and e^x), square root, factorial (x!), and the mathematical constants π and e. Switch between degree and radian angle modes with one button. Full keyboard input is supported — type expressions directly without clicking buttons.
Unlike a basic calculator, this tool uses function notation with parentheses — the same notation used in textbooks and programming. This means you can write nested expressions like sin(pow(2,3)) or ln(sqrt(Math.E)) and get the correct result. Results are accurate to approximately 15 significant digits using JavaScript's IEEE 754 double-precision arithmetic — the same standard used by MATLAB, Python, and all modern scientific software.
Complete function reference — every button explained
- sin, cos, tan: Trigonometric functions. Input is in degrees (DEG mode) or radians (RAD mode). Example: sin(30) in DEG = 0.5. cos(60) in DEG = 0.5. tan(45) in DEG = 1.
- sin⁻¹, cos⁻¹, tan⁻¹ (asin, acos, atan): Inverse trig functions. Give the ratio, get the angle back. Example: asin(0.5) in DEG = 30. atan(1) in DEG = 45. Output is in degrees (DEG) or radians (RAD) depending on mode.
- ln: Natural logarithm — log base e. Used in growth/decay problems, calculus, chemistry (Nernst equation), and physics. Example: ln(e) = 1. ln(1) = 0. ln(100) ≈ 4.60517.
- log: Common logarithm — log base 10. Used in pH calculations (pH = −log[H⁺]), decibels (dB = 10 × log(P₂/P₁)), Richter scale, and signal strength. Example: log(100) = 2. log(1000) = 3. log(1) = 0.
- √ (sqrt): Square root. Example: sqrt(144) = 12. sqrt(2) ≈ 1.41421. Also: sqrt(Math.PI) ≈ 1.7725.
- x^y (pow): Power function — base to the exponent. Syntax: pow(base, exponent). Example: pow(2,10) = 1024. pow(3,4) = 81. pow(Math.E, 2) ≈ 7.389.
- x! (fact): Factorial. Example: fact(5) = 120. fact(10) = 3628800. fact(0) = 1 (by definition). Used in permutations (nPr) and combinations (nCr) in probability and combinatorics.
- e^x (exp): Euler's number raised to the power x. Equivalent to pow(Math.E, x) but more precise. Used in exponential growth/decay: A = A₀ × e^(kt). Example: exp(1) ≈ 2.71828. exp(0) = 1.
- π (pi): The constant 3.14159265358979…. Used as Math.PI internally. Combine with trig: sin(Math.PI/6) in RAD = 0.5 (= sin(30°)).
- e: Euler's number — 2.71828182845905…. The base of natural logarithms. Used as Math.E internally. ln(Math.E) = 1 exactly.
- DEG/RAD toggle: Switches angle interpretation for all trig functions and their inverses. Current mode is shown above the display. For board exams and everyday geometry, use DEG. For calculus, physics formulas, and competitive exams at advanced level, use RAD.
- ( ) brackets: Group sub-expressions or close function calls. Every function (sin, cos, ln, etc.) opens a bracket automatically — you must close it with ) before pressing =.
- , (comma): Separates arguments in the pow() and any two-argument function. Example: pow(2,8) — type: x^y, 2, comma, 8, ), =.
- % (percent): Converts to decimal fraction (÷ 100). 45% = 0.45. Useful for percentage calculations alongside trig.
- +/− (negate): Toggles the sign of the entire current expression. Makes a positive expression negative and vice versa.
- ⌫ (backspace): Deletes the last character or the last full function token (e.g. pressing backspace after "sin(" removes the entire "sin(" not just the "(").
- AC (All Clear): Clears the entire display and resets the input.
- Keyboard shortcuts: Numbers 0–9, operators +, −, *, /, brackets ( ), comma , percentage % all work directly from the keyboard. Enter = calculate. Backspace = delete last. Escape = clear all.
Scientific calculator guide — formulas, examples, and exam applications
Trigonometry — complete guide with standard angle values
Trigonometry is the single most tested topic in Class 10–12 maths, JEE Main, and NEET physics. The six standard angles (0°, 30°, 45°, 60°, 90°, 180°) cover the vast majority of exam questions. Use this calculator to verify your working, and switch to RAD mode when solving calculus or wave-equation problems.
Standard trigonometric values (DEG mode) — memorise these for exams:
- sin(0°) = 0 | sin(30°) = 0.5 | sin(45°) = 0.7071 | sin(60°) = 0.8660 | sin(90°) = 1
- cos(0°) = 1 | cos(30°) = 0.8660 | cos(45°) = 0.7071 | cos(60°) = 0.5 | cos(90°) = 0
- tan(0°) = 0 | tan(30°) = 0.5774 | tan(45°) = 1 | tan(60°) = 1.7321 | tan(90°) = undefined (Infinity)
Try each in the calculator (DEG mode): press sin, type 30, press ), press =. You get exactly 0.5. Press sin, type 45, press ), press = — you get 0.70710678118655 (= 1/√2). These values are used in force resolution (physics), triangle area and height (geometry), and AC circuit analysis (engineering).
Inverse trigonometry — finding the angle from the ratio: If you know sin θ = 0.5 and need θ, press asin (sin⁻¹), type 0.5, press ), press =. Result: 30° (in DEG mode). This is used in: finding the angle of a ramp given its rise and run, finding launch angles in projectile problems, and finding bond angles in chemistry (NEET). Common exam values: asin(1) = 90°, acos(0) = 90°, atan(√3) = 60°, atan(1/√3) = 30°.
DEG vs RAD — when to use each mode
Use DEG for:
Class 10–12 geometry and trigonometry. Navigation and bearing problems. JEE problems that give angles in degrees. NEET physics: inclined planes, force components, angle of projection. Everyday measurement (protractors, compass bearings).
Use RAD for:
Calculus (derivatives and integrals of trig functions). Wave equations: y = A sin(ωt + φ) where ω is in rad/s. JEE Advanced: limits like lim(x→0) sin(x)/x = 1 only works in radians. Simple harmonic motion formulas. Fourier analysis and signal processing.
Converting between them:
Degrees to radians: multiply by π/180. Radians to degrees: multiply by 180/π. Example: 90° = 90 × π/180 = π/2 ≈ 1.5708 rad. In the calculator: pow(90*Math.PI/180, 1) confirms the conversion. sin(π/2) in RAD = 1 = sin(90°) in DEG.
Logarithms — ln vs log, and real-world applications
ln (natural logarithm, base e): The logarithm with base e = 2.71828…. It is the "natural" choice for growth and decay problems because the derivative of eˣ is eˣ itself. Key identities: ln(e) = 1. ln(1) = 0. ln(eⁿ) = n. ln(ab) = ln(a) + ln(b). ln(a/b) = ln(a) − ln(b). ln(aⁿ) = n × ln(a).
Applications: Radioactive decay — N = N₀ × e^(−λt). To find half-life t½ = ln(2)/λ ≈ 0.693/λ. Compound interest — continuous compounding: A = P × e^(rt). Population growth: P = P₀ × e^(kt). Nernst equation (NEET chemistry): E = E° − (RT/nF) × ln(Q). In the calculator: press ln, type 2, press ), press = → 0.693147… This is ln(2), used in every half-life calculation.
log (common logarithm, base 10): The logarithm with base 10. Key identities: log(10) = 1. log(100) = 2. log(1000) = 3. log(1) = 0. log(10ⁿ) = n. Converting between ln and log: ln(x) = log(x) / log(e) = log(x) × 2.302585. log(x) = ln(x) / ln(10) = ln(x) × 0.434294.
Applications: pH (NEET chemistry) — pH = −log[H⁺]. For [H⁺] = 10⁻⁷, pH = −log(10⁻⁷) = 7. In the calculator: press log, type 0.0000001, press ), press = → −7. Decibels (dB) in physics — dB = 10 × log(I/I₀). Richter scale — each unit is 10× more powerful. Signal-to-noise ratio in electronics.
Factorial and combinatorics — probability and permutation problems
Factorial (n!) is the product of all positive integers up to n. By definition, 0! = 1 and 1! = 1. Factorials grow extremely fast:
- 5! = 120 | 6! = 720 | 7! = 5040 | 8! = 40320 | 10! = 3,628,800 | 12! = 479,001,600 | 20! ≈ 2.43 × 10¹⁸
Factorial is the foundation of: Permutations: nPr = n! / (n−r)! — arranging r items from n in order. How many 3-digit PINs from digits 1–9 (no repeat)? 9P3 = 9! / 6! = 504. In calculator: fact(9) / fact(6) = 504. Combinations: nCr = n! / (r! × (n−r)!) — choosing r items from n without caring about order. How many ways to choose 3 students from a class of 30? 30C3 = fact(30) / (fact(3) × fact(27)) = 4060. Binomial theorem (JEE): (a+b)ⁿ coefficients are nCr values. Probability distributions (Poisson, binomial) use n! in their formulas.
Power and exponent calculations
The x^y (pow) function computes any base to any exponent — not just integers. Syntax: pow(base, exponent). Enter as: press x^y, type the base, press comma, type the exponent, press ), press =.
- Integer powers: pow(2,10) = 1024. pow(3,5) = 243. pow(10,6) = 1,000,000.
- Fractional exponents (roots): pow(8, 1/3) = cube root of 8 = 2. pow(16, 0.25) = fourth root of 16 = 2. pow(27, 0.333) ≈ 3. This works for any root — pow(x, 1/n) gives the nth root of x.
- Negative exponents: pow(2, -3) = 1/8 = 0.125. pow(10, -2) = 0.01. Used in scientific notation conversions and unit conversions.
- Irrational exponents: pow(Math.E, Math.PI) ≈ 23.1407. pow(2, Math.PI) ≈ 8.8250. The calculator handles these correctly.
- Physics applications: Gravitational force F = G × m₁m₂ / r² — the r² uses pow(r,2). Coulomb's law: F = kq₁q₂/r² — same pattern. Kinetic energy: KE = ½mv² — use pow(v,2).
The e^x (exp) function is specifically for Euler's number raised to a power — more precise than pow(Math.E, x) for large exponents. exp(0) = 1. exp(1) = 2.71828… exp(10) ≈ 22026. exp(−1) ≈ 0.36788. Used in: continuous compounding (A = Pe^(rt)), radioactive decay, Maxwell-Boltzmann distribution in chemistry/physics.
Using this calculator for JEE, NEET and board exams
NEET Physics/Chemistry
Verify trig values for inclined plane problems. Calculate pH with log. Nernst equation with ln. Radioactive decay half-life with ln(2)/λ. pH: press log, type concentration, ), = → negate result.
JEE Maths
Check trig identity values. Verify log calculations. Calculate nCr with fact(). Cross-check power function results. Switch to RAD for calculus limits: sin(x)/x as x→0 in RAD equals 1.
Board Exams (CBSE/ICSE)
Class 10: trig ratios and standard angles. Class 11: trig equations, log properties, permutations/combinations with fact(). Class 12: calculus check with ln/exp, vectors with magnitude calculations using sqrt and pow.
Worked examples — step by step
Example 1 — Find the angle of a ramp: A ramp rises 3 m over a horizontal distance of 4 m. Find the angle. tan θ = 3/4 = 0.75. Angle = atan(0.75) in DEG. In the calculator: press tan⁻¹, type 0.75, press ), press = → 36.87°. The ramp makes a 36.87° angle with the horizontal.
Example 2 — pH of a solution: [H⁺] = 3.5 × 10⁻⁴ mol/L. pH = −log(3.5 × 10⁻⁴). In the calculator: press log, type 3.5e-4 (type: 3.5 * pow(10,-4)), press ), press = → −3.456. Negate: pH = 3.456 (acidic, as pH < 7).
Example 3 — Radioactive half-life: Carbon-14 has a decay constant λ = 0.000121 per year. Half-life t½ = ln(2)/λ. In calculator: press ln, type 2, press ), press = → 0.693147. Now divide: 0.693147 / 0.000121 = 5728 years (matches the known 5730-year half-life of C-14).
Example 4 — Combinations for probability: A committee of 4 must be chosen from 10 candidates. How many ways? ¹⁰C₄ = 10! / (4! × 6!). In calculator: fact(10) / (fact(4) * fact(6)) → press x!, type 10, ), /, (, x!, 4, ), *, x!, 6, ), ), = → 210.
Example 5 — SHM velocity: In simple harmonic motion, v = ω√(A² − x²). If ω = 5 rad/s, A = 0.1 m, x = 0.06 m: v = 5 × sqrt(pow(0.1,2) − pow(0.06,2)). In calculator: 5 * sqrt(pow(0.1,2) - pow(0.06,2)) → type this expression using the buttons → = → 0.4 m/s.
Free, instant, keyboard-supported — works for every exam function.
Frequently asked questions
How do I calculate sin, cos or tan of an angle?
First, check the mode indicator above the display — it shows either DEG or RAD. Press the DEG/RAD button to switch if needed. For most school and exam problems, use DEG. Then: press the trig button (sin, cos, or tan), type the angle value, press ), and press = or Enter. Examples: sin(30°): Mode=DEG → sin → 30 → ) → = → Result: 0.5. cos(60°): Mode=DEG → cos → 60 → ) → = → Result: 0.5. tan(45°): Mode=DEG → tan → 45 → ) → = → Result: 1. sin(π/2) in radians: Mode=RAD → sin → π (press the π button, it inserts Math.PI) → /2 → ) → = → Result: 1. Key exam values to remember: sin30 = cos60 = 0.5; sin45 = cos45 = 1/√2 ≈ 0.7071; sin60 = cos30 = √3/2 ≈ 0.8660; sin90 = cos0 = 1; tan30 = 1/√3 ≈ 0.5774; tan60 = √3 ≈ 1.7321.
What is the difference between DEG and RAD mode, and which should I use?
DEG (degree) mode and RAD (radian) mode control how the calculator interprets angle inputs and outputs for all trigonometric functions. In DEG mode, sin(90) = 1 because 90° is a right angle. In RAD mode, sin(90) ≈ 0.8940 — because 90 radians is not a right angle; the right angle in radians is π/2 ≈ 1.5708. Getting this wrong is the most common cause of incorrect trig answers. Use DEG when: The problem states angles in degrees (30°, 45°, 90° etc.) — Class 10–12 boards, NEET Physics inclined planes, triangle problems, navigation, bearings. Use RAD when: The problem uses radians (π/2, π/3 etc.) — JEE Advanced calculus, wave equations (y = A sin ωt where ω is angular frequency in rad/s), simple harmonic motion formulas, limits involving trigonometry (lim sin(x)/x = 1 as x→0 is ONLY valid in radians). Quick check: sin(90) in DEG should equal 1. If you see 0.894, you're in RAD mode by mistake. Press DEG/RAD to fix it.
How do I calculate 2 to the power of 10 (2^10)?
Use the x^y (pow) button. Syntax: pow(base, exponent). Steps: press x^y (this types "pow("), type 2, press the , (comma) button, type 10, press ), press =. The display shows: pow(2,10) and the result is 1024. More examples: 3^5: x^y → 3 → , → 5 → ) → = → 243. Cube root of 27 (27^(1/3)): x^y → 27 → , → 1/3 → ) → = → 3. Fractional exponents work: pow(x, 1/n) gives the nth root of x. Negative exponents also work: pow(2,-3) = 0.125 (= 1/8). You can also use e^x (the exp button) specifically for e raised to a power: exp(1) = 2.71828, exp(2) = 7.389, exp(0) = 1.
How do I calculate log and ln (natural logarithm)?
For log (base 10): Press log, type the number, press ), press =. Example: log(1000) → log → 1000 → ) → = → 3 (because 10³ = 1000). log(0.01) → = → −2. For ln (natural log, base e): Press ln, type the number, press ), press =. Example: ln(e) → ln → e (press the e button) → ) → = → 1. ln(1) = 0. ln(100) ≈ 4.6052. To convert between ln and log: ln(x) = log(x) × 2.302585. log(x) = ln(x) × 0.434294. Key NEET chemistry use: pH = −log[H⁺]. For [H⁺] = 10⁻⁴ mol/L: log → 0.0001 → ) → = → −4 → negate (+/−) → pH = 4. Nernst equation: E_cell = E° − (0.0592/n) × log(Q) at 25°C. Calculate log(Q) first, then multiply by (0.0592/n) and subtract from E°.
How do I calculate factorial and combinations (nCr)?
Factorial: Press x!, type the number, press ), press =. Example: fact(7) = 5040. fact(0) = 1 (by definition). fact(12) = 479001600. The calculator handles up to about fact(170) before exceeding JavaScript's number range (returns Infinity for fact(171)+). Combination nCr = n! / (r! × (n−r)!): Use multiple fact() calls. Example: ¹⁰C₄ (choose 4 from 10): type fact(10)/(fact(4)*fact(6)). In buttons: x! 10 ) / ( x! 4 ) * x! 6 ) ) = → 210. Permutation nPr = n! / (n−r)!: Example: ⁸P₃ (arrange 3 from 8): type fact(8)/fact(5). Result: 336. These are heavily tested in JEE Main (probability chapter), CBSE Class 11 (permutations and combinations), and NEET biology (genetics combinations).
Can I type expressions directly from the keyboard?
Yes — full keyboard input is supported. All digit keys (0–9), operators (+, −, *, /), decimal point (.), brackets ( and ), comma (,), and percentage (%) work directly from your keyboard. Press Enter to calculate (same as the = button). Press Backspace to delete the last character or function token (pressing Backspace after "sin(" removes the entire "sin(" in one press — not character by character). Press Escape to clear the display (same as AC). Keyboard input is especially useful for long chained expressions. Note: function buttons (sin, cos, ln, log, etc.) must be clicked with the mouse — they are not assigned to keyboard shortcuts. But once you press sin with the mouse (which types "sin("), you can type the argument and close bracket from the keyboard. Workflow example: click sin with mouse → keyboard type 30 → keyboard press ) → keyboard press Enter → result: 0.5.
How accurate is this calculator? Can I use it for exams?
This calculator uses JavaScript's built-in Math library, which implements IEEE 754 double-precision floating-point arithmetic — the same standard used by Python, MATLAB, Excel, and virtually all scientific software. This gives approximately 15–16 significant decimal places of precision. For context, this is more than sufficient for: all Class 10–12 board exam problems, JEE Main and Advanced calculations, NEET Physics and Chemistry problems, undergraduate engineering coursework, and most professional scientific and engineering calculations. The calculator rounds to 12 significant digits in the display to avoid showing floating-point noise (e.g. 0.100000000000001 displays as 0.1). Rare floating-point quirks to be aware of: sin(180°) displays as approximately 1.22 × 10⁻¹⁶ instead of exactly 0 — this is a known floating-point behaviour (the mathematically correct answer is 0, and the calculator's result is effectively zero for all practical purposes). For critical engineering design or financial calculations, always cross-verify with certified professional tools.