Scientific Calculator

What Is a Scientific Calculator?

A scientific calculator is a powerful mathematical tool that extends the capabilities of a basic four-function calculator. While a standard calculator handles only addition, subtraction, multiplication, and division, a scientific calculator adds an array of advanced mathematical functions that are indispensable in higher education and professional work. These include trigonometric functions (sine, cosine, tangent, and their inverses), logarithms (base-10 and natural), exponential and power operations, square roots and nth roots, factorial computation, and memory storage.

This free online scientific calculator delivers all of those capabilities directly in your web browser. There is nothing to install and no account required. Calculations are processed in-browser, while this page may load third-party services for analytics and ads. Whether you are a student working through trigonometry homework, an engineer verifying a structural calculation, a chemist computing a pH value, or a programmer checking an algorithm, this tool has you covered.

How to Use This Tool

1. Choose your angle mode. Click the DEG button (or the DEG/RAD badge in the display) to toggle between degrees and radians before entering any trigonometric function. The current mode is always visible in both the display and the top-left button.
2. Enter your expression. Click the calculator buttons or type directly using your keyboard. Numbers, operators (+, -, ×, ÷), and parentheses can all be typed from the keyboard.
3. Use function buttons for advanced operations. Click sin(, cos(, tan(, log(, ln(, or √( to start a function. Always close the parenthesis before pressing = or the calculator will close it automatically.
4. Use parentheses to control order of operations. Click ( and ) to group parts of your expression. For example, to compute (3+4)×(2+5), type it exactly as shown.
5. Raise to a power. Type the base number, click xⁿ (which inserts the ^ symbol), and then type the exponent. For example, 2^8 = 256. Use the dedicated x² or x³ buttons for convenience.
6. Calculate square roots. Click the √ button, which inserts √(, then type the number and close with ). For example, √(144) = 12.
7. Compute factorials. Type a non-negative integer, then click n!, which inserts fact(. Close with ) and press =. For example, fact(5) = 120.
8. Use memory. Press MS to save the current result, MR to recall it into the expression, M+ or M− to add or subtract from memory, and MC to clear memory. The current memory value is shown in the M: display at the top-left of the calculator screen.
9. Review history. Every calculation you evaluate is saved to the history panel on the right. Click any history entry to load that result back into the expression field.
10. Press = to evaluate. Click the equals button or press Enter on your keyboard. The result appears immediately in the large gradient display. If there is an error (such as division by zero or an invalid expression), the display shows "Error".

Trigonometric Functions

The three primary trigonometric functions — sine (sin), cosine (cos), and tangent (tan) — relate the angles of a right triangle to the ratios of its sides. In a right triangle, if θ is one of the non-right angles, then:

• sin(θ) = opposite ÷ hypotenuse
• cos(θ) = adjacent ÷ hypotenuse
• tan(θ) = opposite ÷ adjacent = sin(θ) ÷ cos(θ)

These functions are also defined for any real-valued angle via the unit circle, where sin(θ) is the y-coordinate and cos(θ) is the x-coordinate of a point on a circle of radius 1 at angle θ from the positive x-axis. This extension is what makes trigonometry applicable to wave physics, signal processing, and rotational dynamics.

The inverse trigonometric functions — sin⁻¹ (arcsin), cos⁻¹ (arccos), and tan⁻¹ (arctan) — recover the angle given a ratio. For example, sin⁻¹(0.5) = 30° in DEG mode or π/6 in RAD mode. These are invaluable when you know the ratio of sides and need to find the angle.

DEG vs RAD Mode

Angles can be expressed in two common units: degrees and radians. A full circle is 360° or 2π radians. The conversion formula is straightforward: multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees.

Use DEG mode when working with everyday geometry, navigation, architecture, surveying, and most textbook problems at the secondary school level. The buttons in this mode interpret angle inputs as degrees.

Use RAD mode when working in calculus (derivatives and integrals of trig functions are much cleaner in radians), physics (wave equations, angular velocity), or any formula that includes radians natively — such as arc length s = rθ or the simple pendulum period formula. Most programming languages and spreadsheets also default to radians.

Logarithms: log vs ln

A logarithm answers the question: "To what exponent must a given base be raised to produce a certain number?" This calculator provides two logarithm functions:

• log (base-10 logarithm): log(x) answers "10 to what power equals x?" Examples: log(100) = 2, log(1000) = 3, log(1) = 0. Base-10 logarithms appear in the pH scale (pH = −log[H⁺]), the Richter scale for earthquakes, and decibels in acoustics (dB = 10·log(P/P₀)).
• ln (natural logarithm): ln(x) answers "e to what power equals x?", where e ≈ 2.71828. Examples: ln(e) = 1, ln(1) = 0, ln(e²) = 2. Natural logarithms appear in calculus (the derivative of ln(x) is 1/x), compound interest, population growth models, radioactive decay, and entropy formulas in physics and information theory.

The two are related by the change-of-base formula: log(x) = ln(x) / ln(10) ≈ ln(x) / 2.3026.

Powers and Roots

This calculator provides multiple ways to work with powers and roots:

• x² appends ^2 — squaring a number multiplies it by itself. Used constantly in area formulas, physics (kinetic energy = ½mv²), and the Pythagorean theorem (a² + b² = c²).
• x³ appends ^3 — cubing a number gives the volume of a cube with that side length.
• xⁿ appends the ^ operator — lets you raise to any power. For example, 2^10 = 1024, 5^0.5 ≈ 2.236.
• √( computes the square root. √(x) = x^0.5. Useful for distances (Pythagorean theorem), standard deviations in statistics, and quadratic formula solutions.
• Cube root: Use n^(1÷3). For example, 27^(1÷3) = 3. More generally, the nth root of x = x^(1/n).

Factorial and Combinatorics

The factorial of a non-negative integer n, written n!, is the product of all positive integers up to n: n! = n × (n−1) × … × 2 × 1. By definition, 0! = 1.

Factorials appear in combinatorics — the study of counting and arrangement. Key formulas include:

• Permutations (ordered arrangements): P(n, k) = n! / (n−k)!
• Combinations (unordered selections): C(n, k) = n! / (k! × (n−k)!)
• Probability: The probability of arranging n distinct objects is n!

Factorials grow extremely rapidly: 10! = 3,628,800; 20! ≈ 2.4 × 10¹⁸; 170! ≈ 7.3 × 10³⁰⁶. This calculator supports n! for 0 ≤ n ≤ 170; beyond 170, the result overflows JavaScript's number representation (exceeding Number.MAX_VALUE ≈ 1.8 × 10³⁰⁸).

Memory Functions

The five memory functions let you store and retrieve values across calculations, streamlining multi-step problems:

• MS (Memory Store): Evaluates the current expression and saves the result to memory. The M: display updates immediately.
• MR (Memory Recall): Inserts the currently stored memory value into the expression at the cursor position.
• M+ (Memory Add): Evaluates the current expression and adds the result to the stored memory value.
• M− (Memory Subtract): Evaluates the current expression and subtracts the result from the stored memory value.
• MC (Memory Clear): Resets the memory to zero. The M: display reverts to "M: —".

Example workflow: compute 3^2 = 9, press MS to save. Then compute 4^2 = 16, press M+. Memory is now 25. Press MR to insert 25, then √(MR) = √(25) = 5 — the Pythagorean theorem solved using memory!

Order of Operations

All expressions in this calculator follow the standard mathematical order of operations, commonly remembered as PEMDAS:

1. P — Parentheses: Expressions inside ( ) are evaluated first, from innermost to outermost.
2. E — Exponents: Powers and roots (^) are evaluated next, right-to-left.
3. M/D — Multiplication and Division: Evaluated left to right at equal precedence.
4. A/S — Addition and Subtraction: Evaluated last, left to right at equal precedence.

Use parentheses liberally to ensure your intended order. For example, 2+3×4 = 14 (multiplication before addition), but (2+3)×4 = 20 (parentheses force addition first).

Common Use Cases by Field

• Engineering: Structural load calculations, Ohm's law (V = IR), power formulas (P = I²R), resonant frequency (f = 1/(2π√(LC))), signal attenuation in dB.
• Physics: Projectile motion (v² = u² + 2as), wave calculations (λ = v/f), gravitational potential energy (U = mgh), centripetal acceleration (a = v²/r).
• Chemistry: pH = −log[H⁺], Arrhenius equation (k = A·e^(−Ea/RT)), ideal gas law (PV = nRT), Beer–Lambert law (A = εlc).
• Finance: Compound interest (A = P(1+r/n)^(nt)), continuous compounding (A = Pe^(rt)), present value discounting, loan amortization.
• Statistics: Standard deviation formulas, z-scores, normal distribution calculations, combinations for probability (C(n,k)).
• Programming: Bit shift equivalents (2^n), modular arithmetic, floating-point precision checks, hash table size selection (prime powers).

Tips for Efficient Use

• Use the keyboard for fast number entry — digits, operators (+, -, *, /), parentheses, Enter, and Backspace all work natively.
• After pressing = and seeing a result, typing a new number automatically starts a fresh expression; pressing an operator appends it to the result so you can chain calculations.
• Always check that you are in the correct angle mode (DEG or RAD) before evaluating any trig function. The mode indicator is shown in two places — the display badge and the top-left button.
• For very long or complex expressions, use the history panel to scroll back and click any previous result to reuse it.
• The ± button negates the current number quickly. For a raw number in the expression, it toggles the leading minus sign. For a completed sub-expression, it wraps it in (−1)×(...).
• The % button divides by 100 — useful for converting percentages. For example, 75÷100 via the % shortcut gives 0.75.
• Need the Percentage Calculator? It handles percentage increases, decreases, and proportions in a dedicated interface. For converting between measurement units, try the Unit Converter. To calculate durations between dates, visit the Days Between Dates tool.