📏 SI Units & Conversions — Level 2 Engineering Maths

Every engineering measurement needs a unit. Using the wrong unit — or forgetting to convert — can cause catastrophic failure. From the NASA Mars orbiter crash (1999, caused by a metric/imperial mix-up!) to everyday workshop errors, units matter enormously.

Level 2 Core Skill 7 SI base units Metric prefixes Imperial conversions Temperature scales

🧠

Key Words — What Do They Mean?

SI UnitThe standard
scientific unit

Prefixkilo, milli,
mega, etc

Conversion FactorNumber to multiply
or divide by

Two systemsMetric (SI) and Imperial — both still used in UK engineering

Metric (SI): mm, cm, m, km / g, kg, t

Imperial: inch, foot, yard, mile / oz, lb, ton

The metric system is used in science, engineering calculations and international trade. Imperial units are still common in construction, manufacturing and daily life in the UK — so engineers must handle both.

📌 In exams you may be given a mix — always check the units in any question before calculating!

Why it mattersReal consequences of unit errors

NASA Mars orbiter (1999) — crashed because one team used imperial, another metric. $327 million lost.
Gimli Glider (1983) — Air Canada Boeing 767 ran out of fuel mid-flight: kg vs lbs confusion
Workshop errors — machining a part in inches when the drawing is in mm produces scrap
Exams — wrong units = wrong answer, even if the number is right

🔬SI Base Unitsthe 7 fundamentals

📏Prefixeskilo, milli, mega…

📐Metricwithin the system

🏴󠁧󠁢󠁥󠁮󠁧󠁿Imperialinches, feet, lbs

🔄Metric↔Imperialcross-system

🌡️Temperature°C, °F, K

⚙️Engineeringreal examples

🔬

SI Base Units

The International System of Units (SI) has 7 base units. Every other unit in science and engineering is derived from these 7.

🧠

Key Words — What Do They Mean?

Base UnitA fundamental
building block

Derived UnitBuilt from base
units, e.g. m/s

The 7 SI Base UnitsThese are the foundation of all measurement

📌 For Level 2 Engineering, you'll mostly use metre, kilogram, second and ampere. Kelvin appears in thermodynamics. Mole and candela are less common but you should know they exist.

Derived UnitsBuilt from the base units — the ones engineers use every day

Derived Unit	Symbol	What it measures	Made from…
Newton	N	Force	kg·m·s⁻²
Pascal	Pa	Pressure / Stress	N/m² = kg·m⁻¹·s⁻²
Joule	J	Energy / Work	N·m = kg·m²·s⁻²
Watt	W	Power	J/s = kg·m²·s⁻³
Volt	V	Voltage	W/A = kg·m²·s⁻³·A⁻¹
Ohm	Ω	Resistance	V/A = kg·m²·s⁻³·A⁻²
Hertz	Hz	Frequency	s⁻¹ (cycles per second)

💡 Memory trick for Newton: F = ma → force = mass × acceleration → kg × m/s² → N = kg·m·s⁻²

📏

SI Prefixes

Prefixes scale any SI unit up or down by powers of 10. Learn these and you can handle any measurement from nanometres to gigawatts!

🧠

Key Words — What Do They Mean?

PrefixGoes in front
of a unit

ScaleHow big or
small

The Prefix ScaleFrom nano (×10⁻⁹) all the way to Giga (×10⁹)

Full Prefix TableAll prefixes you need for Level 2 Engineering

Prefix	Symbol	Multiplier	Engineering Example
nano	n	× 10⁻⁹ = 0.000000001	45 nm — wavelength of UV light
micro	μ	× 10⁻⁶ = 0.000001	250 μm — human hair diameter
milli	m	× 10⁻³ = 0.001	3.5 mm — bolt thread pitch
centi	c	× 10⁻² = 0.01	2.54 cm = 1 inch
(base)	—	× 10⁰ = 1	1 m, 1 kg, 1 s
kilo	k	× 10³ = 1,000	4.5 kN — cable tension
Mega	M	× 10⁶ = 1,000,000	200 MPa — steel yield stress
Giga	G	× 10⁹ = 1,000,000,000	200 GPa — Young's modulus steel

Converting with prefixesAlways convert to base unit first

Replace the prefix with its multiplier (e.g. k = × 1000)
Multiply or divide to get the base unit
Then convert to the target prefix if needed

4.7 kN → 4.7 × 1000 = 4700 N

250 μm → 250 × 10⁻⁶ = 0.00025 m

0.85 MW → 0.85 × 10⁶ = 850,000 W

Worked ExamplesPrefix conversions step by step

Convert 3.2 km to mm

km→m: 3.2 × 1000 = 3200 m

m→mm: 3200 × 1000 = 3,200,000 mm ✅

Convert 47 mA to A

milli→base: 47 × 10⁻³

Answer: 0.047 A ✅

📏 Try it — SI Prefix ConverterAny prefix to any prefix

Value

From prefix

→

To prefix

👆Try: 4.7 kΩ → Ω · 47 mA → A · 2400 W → kW · 0.1 μF → pF

📐

Metric Conversions

Converting within the metric system — length, mass, area, volume and time. All based on powers of 10, so just multiply or divide.

🧠

Key Words — What Do They Mean?

MetricBased on
powers of 10

ConvertChange to a
different unit

Lengthkm ↔ m ↔ cm ↔ mm — multiply going right, divide going left

💡 Going right (→) = getting smaller units = multiply. Going left (←) = getting bigger units = divide.

Mass conversions

t × 1000 → kg × 1000 → g × 1000 → mg

t ←÷1000 kg ←÷1000 g ←÷1000 mg

1 tonne = 1000 kg 1 kg = 1000 g 1 g = 1000 mg

Convert 4.25 kg to g

kg → g: × 1000

Answer: 4250 g ✅

Area & Volume conversions⚠️ Trickiest — square and cube the conversion factor!

Area: 1 m² = 100² cm² = 10,000 cm²

Area: 1 cm² = 10² mm² = 100 mm²

Vol: 1 m³ = 100³ cm³ = 1,000,000 cm³

Vol: 1 litre = 1000 cm³ = 1000 ml

⚠️ 1 m = 100 cm but 1 m² ≠ 100 cm² — it's 10,000 cm²! Always square or cube the factor!

Time conversionsSeconds, minutes, hours, days — NOT powers of 10!

📌 1 min = 60 s | 1 hour = 60 min = 3600 s | 1 day = 24 hours = 86,400 s

📐 Try it — Metric ConverterLength · Mass · Volume · Time

Value

From

→

To

👆Try: 4.25 kg → g · 2500 mm → m · 1 hour → s · 5 litres → cm³

🏴󠁧󠁢󠁥󠁮󠁧󠁿

Imperial Units

Imperial units are still widely used in UK engineering, construction and everyday life. You must be able to recognise them and convert to metric.

🧠

Key Words — What Do They Mean?

ImperialThe older UK
unit system

Imperial Length

Unit	Abbreviation	Relationship
inch	in or "	base of small lengths
foot	ft or '	1 ft = 12 inches
yard	yd	1 yd = 3 ft = 36 in
mile	mi	1 mile = 1760 yd = 5280 ft

💡 Memory: 12 inches in a foot (12 months, 12 hours — 12 is everywhere!)

Imperial Mass & Volume

Unit	Abbrev.	Relationship
ounce	oz	base of small mass
pound	lb	1 lb = 16 oz
stone	st	1 st = 14 lb
ton (imperial)	t	1 ton = 2240 lb
fluid ounce	fl oz	base of volume
pint	pt	1 pint = 20 fl oz
gallon	gal	1 gallon = 8 pints

⚠️ UK ton vs US ton: Imperial (UK) ton = 2240 lb. US "short ton" = 2000 lb. Metric tonne = 1000 kg ≈ 2205 lb. Always specify which "ton" you mean in engineering!

🔄

Converting Between Metric & Imperial

The conversion factors you MUST know for Level 2 Engineering. Always write the factor as an equation, then multiply or divide.

🧠

Key Words — What Do They Mean?

Cross-systemConverting between
two systems

MethodWrite: X units × conversion factor = Y units. Arrange to solve for what you need.

Visual ScaleHow imperial and metric lengths compare — shown as bars

Conversion Reference TableThe key conversion factors — memorise these!

Quantity	Imperial → Metric	Metric → Imperial
Length	1 inch = 2.54 cm	1 cm = 0.394 inches
Length	1 foot = 30.48 cm = 0.305 m	1 m = 3.281 feet
Length	1 mile = 1.609 km	1 km = 0.621 miles
Length	1 yard = 0.914 m	1 m = 1.094 yards
Mass	1 ounce (oz) = 28.35 g	1 g = 0.035 oz
Mass	1 pound (lb) = 453.6 g = 0.454 kg	1 kg = 2.205 lb
Mass	1 imperial ton = 1016 kg	1 tonne = 0.984 imp. ton
Volume	1 pint = 568 ml	1 litre = 1.76 pints
Volume	1 gallon = 4.546 litres	1 litre = 0.220 gallons

Convert 5 feet 8 inches to metres

Total inches: 5×12 + 8 = 68 inches

× 2.54: 68 × 2.54 = 172.72 cm

Answer: 1.727 m ✅

⚙️ Convert 3.5 kg to pounds (lbs)

Factor: 1 kg = 2.205 lb

Multiply: 3.5 × 2.205 = 7.7175

Answer: 7.72 lb (3 s.f.) ✅

🔄 Try it — Metric ↔ ImperialLength · Mass · Volume

Value

Convert

👆Try: 5 ft → m · 3.5 kg → lb · 26.2 miles → km (marathon) · 1 gallon → L

🌡️

Temperature Conversions

Three scales — Celsius (°C), Fahrenheit (°F) and Kelvin (K). Engineers use all three depending on the application.

🧠

Key Words — What Do They Mean?

KelvinStarts at
absolute zero

Three Temperature ScalesKey reference points shown visually

°C ↔ °F Formulas

°F = (°C × 9/5) + 32

°C = (°F − 32) × 5/9

Convert 25°C to °F

Formula: °F = (25 × 9/5) + 32

Calculate: (25 × 1.8) + 32 = 45 + 32

Answer: 77°F ✅

°C ↔ Kelvin

K = °C + 273.15

°C = K − 273.15

📌 Kelvin is used in thermodynamics formulas (e.g. ideal gas law: PV = nRT). Temperature differences are the same in K and °C — only the zero point shifts.

Convert 350°C to Kelvin

Formula: K = 350 + 273.15

Answer: 623.15 K ✅

🌡️ Try it — Temperature Converter°C · °F · K

Value

From

→

To

👆Try: 25°C → °F · 350°C → K · 150°C → K (gas law) · 212°F → °C

💡 Quick memory: °C to K — just add 273. K to °C — just subtract 273. The 0.15 is only needed for high-precision work.

⚙️

Applications

Where this topic is used in engineering, manufacturing, maintenance and daily life.

🧠

Where You'll See Units

DrawingsDimensions in
mm

RecipesGrams,
litres

🔧Mechanical: Force N→kN. Pressure Pa→MPa. Torque N·m for bolts.
⚡Electrical: mV→V, mA→A, kΩ→Ω. Unit conversion in circuit analysis.
🏗️Construction: mm→m→km. mm²→m². cm³→litres→m³.
🌡️Daily Life: °C↔K. mph↔m/s. kWh on electricity bill.

⚙️

Units in Engineering

Every engineering calculation involves units. Here's where you'll actually need each conversion skill in your exam and on the job.

🧠

Key Words — What Do They Mean?

ConsistencyAll values in
matching units

🔩 Precision Machining

Drawings may mix inches and mm. CNC programs work in mm. A 3/8" drill bit = 3/8 × 25.4 = 9.525 mm. Thread pitch M8 = 1.25 mm = 1.25 × 0.0394 = 0.049 inches.

3/8" drill bit:
3 ÷ 8 = 0.375 inches
0.375 × 25.4 = 9.525 mm

M8 pitch = 1.25 mm
= 1.25 ÷ 25.4 = 0.0492"

⚡ Electrical Engineering

Voltage, current and resistance use SI prefixes constantly. A 4.7 kΩ resistor = 4700 Ω. A 100 μF capacitor = 0.0001 F.

4.7 kΩ = 4.7 × 10³ = 4700 Ω
47 mA = 47 × 10⁻³ = 0.047 A
V = IR = 0.047 × 4700
= 220.9 V

🏗️ Structural Engineering

Forces in kN, stresses in MPa or N/mm² (same thing!), Young's modulus in GPa. Unit consistency in stress calculations is critical.

Stress = Force ÷ Area
F = 4.5 kN = 4500 N
A = 300 mm²
σ = 4500 ÷ 300 = 15 N/mm²
= 15 MPa

🌡️ Thermodynamics

Heat engines, refrigerators and gas laws all use Kelvin. Thermal expansion coefficients use 1/°C or 1/K (same difference in change).

Ideal gas: PV = nRT
T must be in KELVIN
T = 150°C + 273 = 423 K

Expansion: ΔL = L × α × ΔT
ΔT same in °C or K

🔧 Engineering Example — Unit Consistency Check

Problem: Calculate the pressure (Pa) on a piston. Force = 2.4 kN, area = 0.008 m².

Convert: 2.4 kN = 2.4 × 1000 = 2400 N

Formula: P = F ÷ A = 2400 ÷ 0.008

Answer: P = 300,000 Pa = 300 kPa = 0.3 MPa ✅

⚙️ Try it — Engineering Unit ConverterForce · Pressure · Power · Speed

Value

Convert

👆Try: 2.4 kN → N · 300000 Pa → kPa · 70 mph → m/s · 1 kWh → J

🎮

Quick Fire Quiz

10 questions, instant feedback.

⚡ Quick Blitz

Score: 0Streak: 0 🔥Q 1/10

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📝

Practice Questions

15 questions in 3 tiers — Level 2 Engineering style with full working shown.

🟢 Tier 1 — Foundations

Q1

State the SI unit and symbol for: (a) force (b) pressure (c) power

[3]

(a) Newton (N)
(b) Pascal (Pa)
(c) Watt (W)

Q2

Convert: (a) 4.5 km to m (b) 850 mm to m (c) 2.3 cm to mm

[3]

(a) 4.5 × 1000 = 4500 m
(b) 850 ÷ 1000 = 0.85 m
(c) 2.3 × 10 = 23 mm

Q3

Convert: (a) 3.2 kg to g (b) 750 g to kg

[2]

(a) 3.2 × 1000 = 3200 g
(b) 750 ÷ 1000 = 0.75 kg

Q4

Write the prefix and symbol for: (a) × 10⁻³ (b) × 10³ (c) × 10⁶

[3]

(a) milli, m
(b) kilo, k
(c) Mega, M

Q5

Convert 25°C to (a) Fahrenheit (b) Kelvin

[3]

(a) °F = (25 × 9/5) + 32 = 45 + 32 = 77°F
(b) K = 25 + 273.15 = 298.15 K

🟡 Tier 2 — Core Skills

Q6

Convert 47 mA to amperes, then to μA.

[3]

47 mA = 47 × 10⁻³ = 0.047 A
0.047 A = 0.047 × 10⁶ μA = 47,000 μA

Q7

A component is 3.5 inches long. Convert to mm. (1 inch = 25.4 mm)

[2]

3.5 × 25.4 = 88.9 mm ✅

Q8

Convert 5 feet 4 inches to centimetres. (1 inch = 2.54 cm)

[3]

Total inches = 5×12 + 4 = 64 inches
64 × 2.54 = 162.56 cm ✅

Q9

Convert an area of 2.5 m² to cm².

[3]

Remember: 1 m = 100 cm, so 1 m² = 100² cm²

1 m² = 10,000 cm²
2.5 × 10,000 = 25,000 cm² ✅

Q10

Convert 350°F to Celsius.

[2]

°C = (350 − 32) × 5/9 = 318 × 5/9 = 1590/9 = 176.7°C ✅

🔴 Tier 3 — Extension Challenge

Q11

Calculate the stress on a bolt. Force = 8.5 kN, cross-sectional area = 50 mm². Express the answer in (a) N/mm² (b) MPa (c) Pa in standard form.

[5]

F = 8.5 kN = 8500 N
σ = F/A = 8500 ÷ 50 = 170 N/mm²
(a) 170 N/mm²
(b) 170 MPa (1 N/mm² = 1 MPa)
(c) 170 × 10⁶ Pa = 1.70 × 10⁸ Pa ✅

Q12

An engineer in the USA specifies a shaft diameter of 1.375 inches. The UK workshop works in mm. Convert to mm to 2 decimal places. (1 inch = 25.4 mm)

[3]

1.375 × 25.4 = 34.93 mm ✅

Q13

A steel bar is heated from 20°C to 680°C. The coefficient of linear thermal expansion is 12 × 10⁻⁶ /K. The bar is 2.4 m long. Calculate the extension in mm.

[4]

ΔT = 680 − 20 = 660 K
ΔL = L × α × ΔT
= 2.4 × 12×10⁻⁶ × 660
= 0.019008 m
= 19.0 mm ✅

Q14

A fuel tank holds 45 gallons. Calculate its capacity in (a) litres and (b) cm³. (1 gallon = 4.546 litres)

[4]

(a) 45 × 4.546 = 204.57 litres
(b) 204.57 × 1000 = 204,570 cm³ ✅

Q15

An electric motor outputs 2.2 kW at 1450 rpm. Calculate the shaft torque using T = P / ω where ω = 2πn/60. Show all unit conversions.

[5]

P = 2.2 kW = 2200 W
ω = 2π × 1450 ÷ 60 = 151.84 rad/s
T = 2200 ÷ 151.84
= 14.49 N·m ✅

🎯 Score guide: Q1–5 = foundations (14 marks) · Q6–10 = core skills (13 marks) · Q11–15 = extension challenge (21 marks)

📏 SI Units & Conversions — Level 2 Engineering Maths

📋 Units — Quick Reference

Key Words — What Do They Mean?

SI Base Units

📋 SI Units — Quick Reference

Key Words — What Do They Mean?

SI Prefixes

📋 Prefixes — Quick Reference

Key Words — What Do They Mean?

Metric Conversions

📋 Metric Conversions — Quick Reference

Key Words — What Do They Mean?

Imperial Units

📋 Imperial Units — Quick Reference

Key Words — What Do They Mean?

Converting Between Metric & Imperial

📋 Metric ↔ Imperial — Quick Reference

Key Words — What Do They Mean?

Temperature Conversions

📋 Temperature — Quick Reference

Key Words — What Do They Mean?

Applications

Where You'll See Units

Units in Engineering

📋 Engineering Units — Quick Reference

Key Words — What Do They Mean?

🔩 Precision Machining

⚡ Electrical Engineering

🏗️ Structural Engineering

🌡️ Thermodynamics

Quick Fire Quiz

⚡ Quick Blitz

Practice Questions