Scientific Calculator UK - Free Online Advanced Maths Calculator

A scientific calculator is an advanced calculator that can perform mathematical operations beyond basic arithmetic. It includes:

• Trigonometric functions: sin, cos, tan, and their inverses (arcsin, arccos, arctan)
• Logarithms: Common log (base 10) and natural log (base e)
• Powers and roots: Squares, cubes, square roots, and nth roots
• Factorial and combinatorics: n!, permutations, combinations
• Constants: π (pi) and e (Euler's number)
• Statistical functions: Mean, standard deviation, variance

Scientific calculators are essential tools for GCSE, A-Level, and university mathematics in the UK.

Click the DEG/RAD button to toggle between angle modes. The current mode is displayed in the indicator at the top right of the calculator.

• Degrees (DEG): Used in most UK school exams. A full circle = 360°
• Radians (RAD): Used in calculus and higher mathematics. A full circle = 2π radians

Conversion: To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

For example: 90° = 90 × π/180 = π/2 radians

This online scientific calculator is perfect for:

• Homework and coursework
• Revision and exam practice
• Checking your answers
• Learning how to use scientific calculator functions

For actual exams: You must use an approved physical calculator. The JCQ (Joint Council for Qualifications) specifies which calculators are permitted. Popular approved models include:

• Casio fx-83GTX (GCSE)
• Casio fx-85GTX (GCSE, with solar power)
• Casio fx-991EX (A-Level)

Both are logarithms, but with different bases:

log (Common Logarithm):

• Base 10 logarithm
• log(100) = 2 because 10² = 100
• Often written as log₁₀(x)
• Used in chemistry (pH scale), physics (decibels), and engineering

ln (Natural Logarithm):

• Base e logarithm (e ≈ 2.71828)
• ln(e) = 1 because e¹ = e
• Often written as logₑ(x) or ln(x)
• Used in calculus, exponential growth/decay, and compound interest

Relationship: ln(x) = log(x) × ln(10) ≈ log(x) × 2.303

Factorial multiplies a positive integer by all positive integers below it:

• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 4! = 4 × 3 × 2 × 1 = 24
• 1! = 1
• 0! = 1 (by definition)

To calculate: Enter the number, then click the n! button.

Uses: Factorial is essential in probability and statistics for calculating permutations (arrangements) and combinations (selections). For example, the number of ways to arrange 5 people in a queue is 5! = 120.

Inverse trigonometric functions find the angle when you know the trigonometric ratio:

• arcsin (sin⁻¹): If sin(θ) = 0.5, then arcsin(0.5) = 30°
• arccos (cos⁻¹): If cos(θ) = 0.5, then arccos(0.5) = 60°
• arctan (tan⁻¹): If tan(θ) = 1, then arctan(1) = 45°

Important: The notation sin⁻¹ does NOT mean 1/sin. The reciprocal of sin is called cosecant (csc). Similarly for cos⁻¹ and tan⁻¹.

Output ranges:

• arcsin outputs angles from -90° to 90°
• arccos outputs angles from 0° to 180°
• arctan outputs angles from -90° to 90°

Memory functions store values for use in multi-step calculations:

• M+ (Memory Add): Adds the current display value to the memory
• M− (Memory Subtract): Subtracts the current display value from the memory
• MR (Memory Recall): Displays the stored memory value
• MC (Memory Clear): Clears the memory (resets to 0)

Example: To calculate (15 × 3) + (22 × 4):

1. Calculate 15 × 3 = 45
2. Press M+ to store 45
3. Calculate 22 × 4 = 88
4. Press M+ to add 88 to memory (now 133)
5. Press MR to recall the total: 133

The EXP button (also labelled ×10ˣ on some calculators) enters numbers in scientific notation:

How to use:

1. Enter the coefficient (e.g., 6.02)
2. Press EXP
3. Enter the exponent (e.g., 23)

This represents 6.02 × 10²³ (Avogadro's number).

Common scientific notation values:

• Speed of light: 3 × 10⁸ m/s → Enter: 3 EXP 8
• Planck's constant: 6.626 × 10⁻³⁴ J·s → Enter: 6.626 EXP -34
• Mass of electron: 9.109 × 10⁻³¹ kg → Enter: 9.109 EXP -31