How To Use A Scientific Calculator: Functions, BODMAS, Degrees vs Radians

A scientific calculator does much more than add and subtract. It follows the correct order of operations, handles powers and roots, trigonometry, logarithms and more. This guide explains the main functions with simple examples so you can use it confidently for school, university or daily work.

1. Order Of Operations (BODMAS / PEMDAS)

Calculators solve expressions in a fixed order: Brackets, Orders (powers and roots), Division and Multiplication, then Addition and Subtraction. For example, 2 + 3 × 4 equals 14, not 20, because multiplication happens first. If you want the addition first, use brackets: (2 + 3) × 4 = 20. When unsure, add brackets.

2. Powers, Roots And Percentages

Power: 2^3 = 8. The square of a number is x^2 and the square root is √x.
Percentage: 15% of 800 is 800 × 15 / 100 = 120.
Reciprocal: 1/x gives the inverse, for example 1/4 = 0.25.

3. Degrees vs Radians

Trigonometric functions (sin, cos, tan) give different answers depending on the angle mode. In degrees mode, sin(30) = 0.5. In radians mode, sin(30) is about −0.988 because 30 is read as 30 radians. Most school problems use degrees, while calculus and physics often use radians. Always check the DEG/RAD indicator before calculating. A full circle is 360° or 2π radians.

4. Trigonometry Basics

For a right-angled triangle: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent. To find an angle from a ratio, use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹). Example: if sin θ = 0.5, then θ = sin⁻¹(0.5) = 30° in degree mode.

5. Logarithms

log usually means base 10 and ln means natural log (base e ≈ 2.718). For example, log(1000) = 3 and ln(e) = 1. Logs are used in pH, sound levels, compound growth and many science formulas.

6. Solving A Quadratic Equation

For ax² + bx + c = 0, the solutions are x = (−b ± √(b² − 4ac)) / 2a. Example: x² − 5x + 6 = 0 gives a=1, b=−5, c=6, so the discriminant is 25 − 24 = 1 and the roots are x = 3 and x = 2. If the discriminant is negative, there are no real roots.

7. Common Mistakes To Avoid

Forgetting the DEG/RAD mode before using sin, cos or tan.
Typing negative numbers without brackets, for example (−3)² = 9 but −3² = −9.
Not closing brackets, which changes the whole result.
Rounding too early. Keep full precision until the final answer.

Try It Now

Practise these examples in our free Online Scientific Calculator, which supports brackets, powers, trigonometry, logarithms and more directly in your browser.