Scientific Calculator

How to use this calculator

Build an expression with the buttons and press = to evaluate it. Use sin, cos, tan (and their inverses sin⁻¹, cos⁻¹, tan⁻¹), ln and log for logarithms, √ and xʸ for roots and powers, and the constants π and e. Switch between Degrees and Radians before entering any angle, use ⌫ to delete the last character, and C to clear the entire expression.

What a scientific calculator does

A basic calculator handles the four arithmetic operations: addition, subtraction, multiplication, and division. A scientific calculator extends that with functions essential for higher mathematics and the sciences:

• Exponents and roots — xʸ raises x to any power y; x² squares quickly; √ takes the square root. These appear in everything from the Pythagorean theorem to compound interest.
• Trigonometric functions — sin, cos, and tan relate angles to side lengths in right triangles and appear throughout physics, engineering, and navigation.
• Inverse trig functions — sin⁻¹, cos⁻¹, tan⁻¹ (arcsin, arccos, arctan) find an angle when you know the ratio of two sides.
• Logarithms — log (base 10) and ln (base e, the natural log) are inverses of exponentiation and appear in chemistry (pH), acoustics (decibels), finance, and calculus.
• Factorials — n! is the product of all positive integers up to n. Used in combinatorics, probability, and the calculation of permutations.
• Constants — π ≈ 3.14159 (ratio of circumference to diameter) and e ≈ 2.71828 (base of the natural logarithm, the number of natural growth) are built in so you never have to type them.

Order of operations

All expressions are evaluated following PEMDAS (also called BODMAS): Parentheses first, then Exponents, then Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. This means 3 + 2 × 4 = 11, not 20, because the multiplication happens before the addition. Wrapping part of an expression in parentheses forces it to be evaluated first.

Degrees vs. radians

Angles can be measured in degrees (a full circle = 360°) or radians (a full circle = 2π ≈ 6.283). The toggle at the top of the calculator controls which unit the trig functions use. A common mistake is leaving the calculator in radian mode when working with everyday angles in degrees — sin(90) in radian mode gives sin(90 rad) ≈ 0.894, not 1. Switch to Degrees mode and sin(90°) correctly returns 1.

To convert: degrees × (π ÷ 180) = radians. So 90° = 90 × π/180 = π/2 ≈ 1.5708 rad.

Worked examples

• sin(30°) = 0.5 — the opposite side of a 30-60-90 triangle is half the hypotenuse.
• cos(60°) = 0.5
• tan(45°) = 1 — at 45°, opposite and adjacent sides are equal.
• 2 xʸ 10 = 1,024 — useful for memory sizes and binary arithmetic.
• √(144) = 12
• log(1000) = 3, because 10³ = 1,000.
• ln(e) = 1, by definition.
• 5! = 120
• (3 + 4) × 2 = 14 — the parentheses force the addition before the multiplication.
• π × 5² = π × 25 ≈ 78.54 — the area of a circle with radius 5.

Common mistakes to avoid

• Wrong angle mode. Always check whether the calculator is in Degrees or Radians before entering trig functions. This is the single most common source of wrong answers.
• Missing parentheses around function arguments. sin 30 + 60 may be parsed as sin(30) + 60, not sin(90). When in doubt, add explicit parentheses: sin(30 + 60).
• Confusing log and ln. log(100) = 2 (base 10). ln(100) ≈ 4.605 (base e). They are not interchangeable; use the one your formula calls for.
• Expecting exact values for irrational results. π, √2, and most trig values are irrational. The calculator shows rounded decimals — for proofs and symbolic work, leave values in exact form.