Physical Quantities, Units and Measurement
Every calculation in Physics depends on getting the units right, and a large share of lost marks across the whole subject trace back to this one topic — unconverted prefixes, mismatched units, and answers with no unit at all.
1. Physical quantities
A physical quantity is something that can be measured, and it always has a number and a unit.
“5 metres” is a physical quantity. “A ruler” is not — it is an object.
A physical quantity is not a visible object. Confusing the two was a recorded error. Length, mass, time and current are quantities; rulers, blocks and wires are things.
2. SI base units
There are seven base units; five matter at IGCSE:
| Quantity | Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
The unit of current is the ampere (A), not the second. That specific confusion was recorded — current is measured in amps; time in seconds.
The base unit of mass is the KILOGRAM, not the gram — the only base unit with a prefix built in.
Derived units
Derived units are built from base units by multiplication or division.
| Quantity | Derived unit | In base units |
|---|---|---|
| Force | newton (N) | kg m/s² |
| Energy / work | joule (J) | kg m²/s² |
| Power | watt (W) | kg m²/s³ |
| Pressure | pascal (Pa) | kg/(m s²) |
| Speed | — | m/s |
| Density | — | kg/m³ |
The newton is a DERIVED unit, not a base unit. Identifying it as fundamental was a recorded error. It comes from F = ma: kg × m/s² = kg m/s².
Working out a derived unit: substitute the base units into the formula and simplify.
Cancel units carefully, exactly as you would cancel algebra. Several recorded errors came from cancelling a unit that appeared on the same side of the fraction, or from putting a quantity in the wrong position in the formula. Write the units out in full, then cancel — and check the final unit is the one you expect.
3. Prefixes and standard form
| Prefix | Symbol | Multiplier | |
|---|---|---|---|
| giga | G | 10⁹ | 1 000 000 000 |
| mega | M | 10⁶ | 1 000 000 |
| kilo | k | 10³ | 1000 |
| centi | c | 10⁻² | ÷100 |
| milli | m | 10⁻³ | ÷1000 |
| micro | µ | 10⁻⁶ | ÷1 000 000 |
| nano | n | 10⁻⁹ |
Convert prefixes to base units BEFORE calculating. This is the most valuable habit in the whole subject — kilometres to metres, milliamps to amps, minutes to seconds.
Common conversions:
- 1 km = 1000 m
- 1 cm = 0.01 m; 1 m = 100 cm
- 1 mm = 0.001 m; 1 cm = 10 mm
- 1 g = 0.001 kg; 1 kg = 1000 g
- 1 minute = 60 s; 1 hour = 3600 s
- 1 cm³ = 1 ml; 1000 cm³ = 1 litre
Positive powers make things bigger; negative powers make them smaller. Confusing the direction was recorded — and so was converting when no conversion was needed. Ask: should this number get bigger or smaller?
Convert all times to seconds unless the question clearly wants otherwise. Failing to convert minutes to hours (or seconds) was recorded repeatedly.
Standard form: write numbers as a × 10ⁿ with 1 ≤ a < 10. So 0.00045 m = 4.5 × 10⁻⁴ m.
4. Measuring length
| Instrument | Use | Precision |
|---|---|---|
| Ruler / metre rule | everyday lengths | 1 mm |
| Measuring tape | long or curved distances | 1 mm |
| Micrometer | very small thicknesses | 0.01 mm |
| Callipers | diameters | 0.1 mm |
Reading a ruler correctly:
Look straight down on the scale. Viewing at an angle causes a parallax error.
Measure from the zero mark, not the end of the ruler, which is often worn.
Measuring something small — the multiple method:
To find the thickness of one sheet of paper, measure a stack of 100 sheets and divide by 100.
The same trick gives the diameter of a wire (wind 20 turns round a pencil, measure the length, divide by 20) or the period of a pendulum (time 20 swings, divide by 20).
This reduces the percentage error, because the measuring uncertainty is spread over many items. It is the standard answer to “how would you improve the accuracy of this measurement?”
You cannot measure one sheet of paper with a ruler, or use a balance for thickness. Both were recorded suggestions. The multiple method is what the mark scheme wants.
Measuring a curved line: lay a piece of string along the curve, mark it, then straighten the string against a ruler.
A tape measure or string-and-ruler measures a circumference — a calculator does not. Suggesting a calculator as a measuring instrument was a recorded error: the question asks for a technique.
5. Measuring volume
Regular solid: measure the sides and calculate — for a cuboid, l × w × h.
Liquid: use a measuring cylinder.
Read the bottom of the meniscus, with your eye level with it.
Irregular solid — the displacement method:
- Part-fill a measuring cylinder with water and record the volume V₁
- Lower the object in, fully submerged
- Record the new volume V₂
- Volume of object = V₂ − V₁
The object must be fully submerged and must sink. For a floating object, push it under with a thin rod, or use a displacement (eureka) can and collect the overflow.
Read the scale carefully — misreading the measuring cylinder scale was a recorded error, as was mishandling the subtraction and the averaging of repeats.
Units: 1 cm³ = 1 ml, and 1000 cm³ = 1 litre = 1 dm³.
6. Measuring time
Use a stopwatch or, for greater precision, light gates.
Human reaction time (~0.2 s) is the main source of error with a stopwatch. Reduce its effect by timing many oscillations and dividing.
Example: 20 swings of a pendulum take 32.0 s → period = 32.0 ÷ 20 = 1.6 s.
Convert stopwatch readings correctly. A reading of 1:30 is 90 s, not 1.30 s — a recorded error.
7. Accuracy, precision and error
- Accurate — close to the true value
- Precise — repeat readings are close to each other
- Zero error — the instrument doesn’t read zero when it should; subtract it from every reading
- Parallax error — caused by viewing a scale at an angle
- Anomalous result — a reading that doesn’t fit the pattern; repeat it and exclude it from the mean
To improve reliability: repeat readings and take a mean; use an instrument with a smaller scale division; measure multiples and divide.
8. Mistakes that cost marks
Leaving the unit off an answer.
Not converting prefixes before calculating.
Confusing positive and negative powers of ten.
Converting when no conversion was needed.
Calling the newton a base unit.
Giving the wrong unit for current.
Cancelling units incorrectly when deriving a unit.
Substituting into a formula in the wrong position.
Measuring one small object instead of using the multiple method.
Misreading a measuring cylinder, or reading the top of the meniscus.
Parallax error from viewing a scale at an angle.
Misconverting stopwatch times.
Frequently asked questions
What is a physical quantity? Something that can be measured — it has a number and a unit.
What are the SI base units? For IGCSE: metre, kilogram, second, ampere and kelvin.
Is the newton a base unit? No — it is derived: 1 N = 1 kg m/s².
How do I find a derived unit? Substitute the base units into the formula and simplify.
How do I convert km to m? Multiply by 1000.
How do I measure the thickness of one sheet of paper? Measure a stack of 100 and divide by 100.
How do I find the volume of an irregular solid? Displacement: submerge it in a measuring cylinder and take the difference in water level.
How do I measure a curved length? Lay string along it, then measure the string with a ruler.
What is parallax error? An error from reading a scale at an angle instead of straight on.
How can I reduce the effect of reaction time? Time many oscillations and divide by the number.
Quick revision checklist
- I know a quantity has a number and a unit
- I know the SI base units and their symbols
- I know the newton is derived, and can express it in base units
- I can work out derived units by substitution and cancelling
- I know the prefixes and can convert both ways
- I convert to base units before calculating
- I can write numbers in standard form
- I can choose the right instrument for a length
- I use the multiple method for small quantities
- I can measure a curved length with string
- I can find volume by displacement
- I read a meniscus at eye level
- I can time oscillations and divide
- I know accuracy vs precision, and zero and parallax error
- I always write the unit on my answer
These notes cover physical quantities, units and measurement techniques in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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