Key Formulas
This page provides a summary of common formulas that are useful for Functional Skills Maths Level 2. Remember to understand when and how to use each formula, not just memorize it.
Units are very important! Always ensure your units are consistent before performing calculations.
Area & Perimeter
Perimeter of Rectangle = 2 × (length + width)
The total distance around a rectangle.
Example: If length = 10cm, width = 5cm, Perimeter = 2 × (10 + 5) = 30cm.
Area of Rectangle = length × width
The space covered by a rectangle.
Example: If length = 10cm, width = 5cm, Area = 10 × 5 = 50cm².
Perimeter of Square = 4 × side
The total distance around a square.
Example: If side = 6m, Perimeter = 4 × 6 = 24m.
Area of Square = side²
The space covered by a square.
Example: If side = 6m, Area = 6² = 36m².
Area of Triangle = 1⁄2 × base × height
Or (base × height) ÷ 2. Height must be perpendicular to the base.
Example: If base = 8cm, height = 5cm, Area = 0.5 × 8 × 5 = 20cm².
Area of Parallelogram = base × perpendicular height
The space covered by a parallelogram.
Example: If base = 7m, height = 4m, Area = 7 × 4 = 28m².
Area of Trapezium = 1⁄2 × (a + b) × height
Where 'a' and 'b' are the lengths of the parallel sides, and 'h' is the perpendicular height between them.
Example: If a = 5cm, b = 7cm, height = 4cm, Area = 0.5 × (5 + 7) × 4 = 24cm².
Circumference of Circle = π × diameter
Or 2 × π × radius. (π ≈ 3.14 or 3.142)
Example: If diameter = 10cm, Circumference ≈ 3.14 × 10 = 31.4cm.
Area of Circle = π × radius²
The space covered by a circle. (π ≈ 3.14 or 3.142)
Example: If radius = 3m, Area ≈ 3.14 × 3² = 3.14 × 9 = 28.26m².
Volume
Volume of Cuboid = length × width × height
The space occupied by a rectangular box.
Example: If l=5cm, w=3cm, h=2cm, Volume = 5 × 3 × 2 = 30cm³.
Volume of Cube = side³
The space occupied by a cube.
Example: If side = 4m, Volume = 4³ = 64m³.
Volume of Cylinder = π × radius² × height
The space occupied by a cylinder. (Area of circular base × height). (π ≈ 3.14 or 3.142)
Example: If r=2cm, h=10cm, Volume ≈ 3.14 × 2² × 10 = 125.6cm³.
Volume of Prism = Area of cross-section × length
Applies to any prism (e.g., triangular prism, hexagonal prism).
Example: Triangular prism with cross-section area 15cm² and length 10cm, Volume = 15 × 10 = 150cm³.
Percentages
Percentage of an Amount = (Percentage ÷ 100) × Amount
Example: 20% of £50 = (20/100) × 50 = 0.2 × 50 = £10.
Percentage Increase = (Increase ÷ Original Amount) × 100%
Where Increase = New Value - Original Value.
Example: Price goes from £50 to £60. Increase = £10. % Increase = (10 / 50) × 100% = 20%.
Percentage Decrease = (Decrease ÷ Original Amount) × 100%
Where Decrease = Original Value - New Value.
Example: Price goes from £50 to £40. Decrease = £10. % Decrease = (10 / 50) × 100% = 20%.
Finding Original Amount (after % increase) = New Amount ÷ (1 + Percentage Increase as decimal)
Example: If price increased by 10% to £55, original = £55 ÷ 1.10 = £50.
Finding Original Amount (after % decrease) = New Amount ÷ (1 - Percentage Decrease as decimal)
Example: If price decreased by 20% to £80, original = £80 ÷ 0.80 = £100.
Speed, Distance, Time
Speed = Distance ÷ Time
Example: If Distance = 100 miles, Time = 2 hours, Speed = 100 ÷ 2 = 50 mph.
Distance = Speed × Time
Example: If Speed = 60 km/h, Time = 3 hours, Distance = 60 × 3 = 180 km.
Time = Distance ÷ Speed
Example: If Distance = 200 m, Speed = 10 m/s, Time = 200 ÷ 10 = 20 seconds.
Density, Mass, Volume
Density = Mass ÷ Volume
Example: If Mass = 100g, Volume = 20cm³, Density = 100 ÷ 20 = 5 g/cm³.
Mass = Density × Volume
Example: If Density = 2 g/cm³, Volume = 50cm³, Mass = 2 × 50 = 100g.
Volume = Mass ÷ Density
Example: If Mass = 80g, Density = 4 g/cm³, Volume = 80 ÷ 4 = 20cm³.
Simple & Compound Interest
Simple Interest (I) = P × R × T
P = Principal, R = Annual Rate (as decimal), T = Time (in years).
Example: P=£100, R=5% (0.05), T=2 years. I = 100 × 0.05 × 2 = £10.
Total Amount (Simple Interest) = P + I
Example: Using above, Total = £100 + £10 = £110.
Total Amount (Compound Interest) = P(1 + R)T
P = Principal, R = Rate per compounding period (as decimal), T = Number of compounding periods. If compounded annually, R is annual rate, T is years.
Example: P=£100, R=5% (0.05) annually, T=2 years. A = 100(1 + 0.05)² = 100 × 1.1025 = £110.25.
Compound Interest Earned = Total Amount - Principal
Example: Using above, CI = £110.25 - £100 = £10.25.
Averages & Range
Mean = Sum of all values ÷ Number of values
Example: Data: 2, 4, 6. Mean = (2+4+6) ÷ 3 = 12 ÷ 3 = 4.
Range = Largest value - Smallest value
Example: Data: 2, 4, 9. Range = 9 - 2 = 7.
Median: The middle value when data is ordered. Example: Data: 1, 3, 7, 8, 9. Median is 7.
Mode: The most frequent value. Example: Data: 2, 3, 3, 4, 5. Mode is 3.