Scientific Calculator

Scientific Calculator: Beyond Four Functions

A scientific calculator handles trig, logs, powers, and special functions, the math required for high school physics, engineering coursework, statistics, and any technical work above basic arithmetic. This in-browser version covers the standard scientific calculator feature set without installing anything.

Function Categories

Trigonometric

• sin(x), cos(x), tan(x), sine, cosine, tangent.
• asin(x), acos(x), atan(x), inverse trig functions.
• sinh(x), cosh(x), tanh(x), hyperbolic trig.
• Mode-dependent: degrees or radians. Default degrees here.

Useful identities to remember:

• sin²(x) + cos²(x) = 1
• tan(x) = sin(x) / cos(x)
• sin(90° − x) = cos(x)

Logarithmic / Exponential

• ln(x), natural log (base e).
• log(x), log base 10.
• e^x, exponential.
• 10^x, power of 10.

For other bases: log_b(x) = ln(x) / ln(b).

Common scales using logarithms:

• dB (decibels) in audio: dB = 10 × log10(P/P_ref).
• pH in chemistry: pH = -log10([H+]).
• Richter scale for earthquakes (each whole number = 10× energy).
• Stellar magnitude in astronomy.

Power and Root

• x^y, x to the power of y. For non-integer y, requires positive base.
• √x (sqrt), square root.
• ∛x (cbrt), cube root.
• x^(1/n), nth root.

x^0.5 = √x. Negative bases with fractional exponents are complex (no real result): (-1)^0.5 = i.

Factorial

• n! = n × (n−1) × ... × 2 × 1.
• 0! = 1 (convention).
• Only defined for non-negative integers in basic form; the Gamma function extends factorial to non-integers (Γ(n+1) = n!).
• Grows fast: 10! = 3,628,800; 20! ≈ 2.4 × 10^18; 170! overflows IEEE 754 doubles.

Constants

• π (pi) ≈ 3.14159, ratio of circumference to diameter.
• e ≈ 2.71828, base of natural log, limit of (1 + 1/n)^n.
• φ (phi) ≈ 1.61803, golden ratio, (1 + √5) / 2.

The Order of Operations

Standard PEMDAS / BODMAS:

1. Parentheses / Brackets.
2. Exponents / Orders (powers, roots).
3. Multiplication and Division (left to right).
4. Addition and Subtraction (left to right).

Examples:

• 2 + 3 × 4 = 2 + 12 = 14 (not 5 × 4 = 20).
• (2 + 3) × 4 = 5 × 4 = 20.
• 2 + 3 × 4^2 = 2 + 3 × 16 = 2 + 48 = 50.
• 6 / 2 × 3 = (6/2) × 3 = 3 × 3 = 9 (left to right for same-precedence).
• 6 / (2 × 3) = 6 / 6 = 1.

When in doubt, add parentheses. Mathematicians and calculators agree they make intent unambiguous.

Floating-Point Reality

JavaScript (and most languages) uses IEEE 754 double-precision floats. Key implications:

~15 significant decimal digits. Beyond that, the bits run out: 1 + 1e-16 = 1 (the addition is below the precision threshold).

Some decimals aren't exact. 0.1 in binary is a repeating fraction, like 1/3 in decimal. The closest double to 0.1 is approximately 0.1000000000000000055511151231257827021181583404541015625. So:

Not a bug, fundamental to binary floating-point.

Catastrophic cancellation. Subtracting two nearly-equal numbers loses precision: 1.0000001 - 1 = 0.0000001, but each operand has 15 digits of precision and the result has only 7.

Infinity and NaN. 1/0 = Infinity. 0/0 = NaN. Infinity - Infinity = NaN. NaN propagates: NaN + x = NaN for any x.

For financial calculations, use decimal libraries (Decimal.js, BigDecimal in Java). For science/engineering, floats are usually fine, just be aware of the limits.

Common Computations

Pythagorean

Right triangle with legs a, b: hypotenuse c = √(a² + b²).

Compound interest

A = P × (1 + r/n)^(n×t) where P is principal, r is rate, n is compounding periods per year, t is years.

Standard deviation

For a sample: s = √(Σ(x − x̄)² / (n−1)). Calculate term by term with the calculator.

Angle of elevation

Looking up at a point: tan(θ) = opposite / adjacent, so θ = atan(opp / adj).

Light intensity at distance

Inverse-square: I = I_0 / d². Doubling distance quarters intensity.

Memory / History

Most scientific calculators include:

• Last result (often Ans key): use the previous result in the next expression.
• History of past calculations.
• Variables (M+, M-, MR, MC) for storing values across calculations.

This calculator includes a history; recent calculations are clickable to reuse.

Common Mistakes

Mixing degrees and radians. The classic. sin(90) in radians ≈ 0.894; in degrees = 1. Always confirm mode.

Forgetting parentheses with negative exponents. -2^2 is interpreted as -(2^2) = -4 by most calculators. For (-2)^2 = 4, write explicitly with parens.

Computing logarithms wrong base. log could be base 10 or natural depending on context. ln is always natural. Be explicit.

Order of factorial vs power. 2^3! is ambiguous; usually evaluated as 2^(3!) = 2^6 = 64, not (2^3)! = 8! = 40320.

Implicit multiplication ambiguity. 6 / 2(1+2) is famously ambiguous online, different calculators give 1 or 9. Just use explicit / and * with parens.

Rounding accumulating. Computing a long chain step-by-step can accumulate error. For high precision, do as much in one expression as possible.

When You Need More

Scientific calculators max out at:

• 15-16 digit precision.
• Common math functions.
• Simple expressions.

For more, you need:

• Programming calculator / REPL: Python with NumPy, Julia, R for arbitrary precision and complex calculations.
• Symbolic math: WolframAlpha, SymPy, Mathematica for symbolic manipulation (algebraic simplification, calculus).
• Specialized calculators: graphing calculators for visualization (Desmos, GeoGebra are free in-browser).
• Spreadsheets: Excel/Sheets for tabular computations.

This calculator is for quick scientific calculations during work, study, or exploration, not heavy numerical analysis.

Privacy

All math runs in your browser using JavaScript's Math library plus a small expression parser. The expressions you enter and results never leave the page. Open DevTools Network during use: zero outbound requests. Sometimes the numbers being calculated are sensitive, financial figures, research data, confidential figures. They stay in the tab.