Math

Scientific Calculator

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DEG

Scientific

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Tip: use parentheses for nested expressions like (5+2)×(3/2). The math.js engine guarantees high-precision decimal arithmetic.

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Quick summary

Evaluate expressions with trig, logs, roots, and constants.

How to calculate scientific manually

Enter your input values into the Scientific calculator above.
Review the formula and assumptions in the Expert Guide section.
Adjust the inputs to model different scenarios in real time.
Save or export the results once they match your scenario.

Evaluate expressions with trig, logs, roots, and constants.

How it works

Supports + − × ÷ ^, parentheses, sin/cos/tan/asin/acos/atan, log, ln, sqrt, cbrt, abs, exp, pi, e.

Example

sin(pi/4) + sqrt(16) × 2 ≈ 8.7071.

Technical guide

Understanding scientific notation and trigonometric functions

A pro-grade scientific calculator handles three things a basic calculator cannot: very large or very small numbers via scientific notation, angle-aware trigonometry, and nested expressions with exact operator precedence. Here's how to read the display and combine those features for real engineering, physics, and statistics work.

Scientific notation: reading 1.2 × 10¹⁵ correctly

Scientific notation expresses any number as a coefficient between 1 and 10 multiplied by a power of ten. The display 1.2 × 10¹⁵ means 1,200,000,000,000,000 — 1.2 quadrillion. Negative exponents shift the decimal left: 6.022 × 10⁻²³ is 0.00000000000000000000006022. Calcly automatically switches to scientific notation when a result exceeds 10¹² or falls below 10⁻⁶, which keeps long answers readable while preserving 12 significant digits of precision under the hood. Example 1: compute Avogadro's number times 0.5 mol — type 6.022e23 * 0.5 and the display returns 3.011 × 10²³. Example 2: light's travel time across a 1 mm gap — type 0.001 / 3e8 to get 3.333 × 10⁻¹².

Trigonometry, DEG vs. RAD, and inverse functions

Every trig answer depends on the angle mode. In DEG mode, sin(30) returns 0.5; in RAD mode the same input returns −0.988 because the calculator interprets 30 as 30 radians. The DEG/RAD indicator at the top of the display always reflects the active mode. Inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) reverse the operation and respect the same mode — sin⁻¹(0.5) returns 30 in DEG mode and 0.5236 (≈ π/6) in RAD mode. Press SHIFT to expose the inverse row. Example 3: solve a right triangle where the opposite side is 7 and the hypotenuse is 25 — switch to DEG, type sin⁻¹(7/25), and the display reads 16.26°.

Nested expressions and operator precedence

Parentheses are not decorative — they control the order of operations. The expression (5+2)×(3/2) evaluates the two parenthesized blocks first, then multiplies, returning 10.5. Without parentheses, 5+2×3/2 follows PEMDAS and returns 8. The math.js engine powering this calculator uses IEEE-754 double precision plus exact-fraction shortcuts where possible, so chained operations like (1.1 + 2.2) − 3.3 return a clean 0 instead of the floating-point glitch (4.440892098500626 × 10⁻¹⁶) you'd see in raw JavaScript. Combine this with absolute value |x|, powers x^y, and roots √x to build expressions like sqrt(|−9|) × (2^10) in a single line.

Frequently asked questions

What's the difference between log and ln?

log is the base-10 logarithm — log(1000) = 3 because 10³ = 1000. ln is the natural logarithm with base e (≈ 2.71828) — ln(e) = 1, and ln(7.389) ≈ 2. Use log for orders of magnitude (decibels, pH, Richter scale) and ln for continuous growth, decay, and calculus.

When should I switch from DEG to RAD?

Use DEG for everyday geometry, surveying, and most engineering drawings where angles are quoted in degrees. Switch to RAD for calculus, physics formulas involving angular velocity or wave equations, and any expression that mixes π directly with a trig function — for example sin(π/6) only returns 0.5 in RAD mode.

How accurate is the math engine?

Calcly uses math.js, which provides 64-bit IEEE-754 floating-point arithmetic with up to 15 significant digits, plus BigNumber and Fraction types for exact rational results when applicable. For the vast majority of scientific work — through statistics, finance, and undergraduate physics — the precision exceeds what a Casio fx-991 or TI-30X II delivers.