Units & Measures
Measurements describe the physical world. Understanding unit conversions, compound measures (speed, density, pressure), and time calculations is essential in science, engineering, and everyday life.
Speed: distance ÷ time (m/s, km/h, mph)
Density: mass ÷ volume (g/cm³, kg/m³)
Pressure: force ÷ area (N/m², Pa)
Population density: people ÷ area (per km²)
📖 Learn
Metric Unit Conversions
Length:
1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
Mass:
1 tonne = 1000 kg
1 kg = 1000 g
1 g = 1000 mg
Capacity:
1 litre = 1000 ml
1 cl = 10 ml
1 m³ = 1000 litres
Area:
1 cm² = 100 mm²
1 m² = 10000 cm²
1 km² = 1000000 m²
Volume:
1 cm³ = 1 ml
1 litre = 1000 cm³
1 m³ = 1000000 cm³
💡 To convert larger → smaller units: multiply. Smaller → larger: divide.
Imperial Units (approximate conversions)
1 inch ≈ 2.54 cm
1 foot = 12 inches
1 mile ≈ 1.6 km
1 pound ≈ 450 g
1 stone = 14 pounds
1 ounce ≈ 28 g
1 gallon ≈ 4.5 litres
1 pint ≈ 0.57 litres
Speed, Distance and Time
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Converting speeds: km/h → m/s: ÷ 3.6 m/s → km/h: × 3.6
Remember to use consistent units: if speed is in km/h, distance must be in km and time in hours.
💡 Use the SDT triangle: cover the quantity you want to find. S = D/T, D = S×T, T = D/S
Density and Pressure
Density = Mass ÷ Volume (g/cm³ or kg/m³)
Mass = Density × Volume
Volume = Mass ÷ Density
Pressure = Force ÷ Area (N/m² or Pa)
Force = Pressure × Area
Water has density ≈ 1 g/cm³. Gold ≈ 19.3 g/cm³. Aluminium ≈ 2.7 g/cm³.
Time Calculations
Time is in hours, minutes, seconds. There are 60 seconds in a minute and 60 minutes in an hour.
- 2 hours 30 minutes = 2.5 hours
- 1 hour 15 minutes = 1.25 hours
- 45 minutes = 0.75 hours
- 20 minutes = 20/60 = 1/3 hour ≈ 0.333 hours
💡 When calculating with speed/distance/time, always convert time to decimal hours first.
✏️ Worked Examples
Example 1: Unit conversion (area)
Convert 3.5 m² to cm².
1 m = 100 cm, so 1 m² = 100² cm² = 10000 cm²
3.5 × 10000 = 35000 cm²
Example 2: Speed calculation
A car travels 240 km in 3 hours. Find its average speed in km/h, then convert to m/s.
Speed = D ÷ T = 240 ÷ 3 = 80 km/h
Convert: 80 ÷ 3.6 = 22.2 m/s (1 d.p.)
Example 3: Density
A block of aluminium has mass 540 g and volume 200 cm³. Find its density.
Density = Mass ÷ Volume = 540 ÷ 200 = 2.7 g/cm³
Example 4: Time and distance
A train travels at 120 km/h. How long does it take to travel 90 km? Give answer in minutes.
Time = D ÷ S = 90 ÷ 120 = 0.75 hours
0.75 × 60 = 45 minutes