Physical Quantities, Units and Measurement: Complete O Level Physics Cheatsheet

Base quantities and SI units

A base quantity is one of a small set of physical quantities that cannot be defined in terms of other quantities. At O Level, you need to know 5: mass, length, time, electric current, and temperature.

Base quantities and their SI units: mass (kilogram, kg), length (metre, m), time (second, s), electric current (ampere, A), temperature (kelvin, K).

A derived quantity is any physical quantity formed by combining base quantities, e.g. speed = distance ÷ time (m/s), density = mass ÷ volume (kg/m³), force = mass × acceleration (N).

Trick: If you're ever unsure whether a unit is 'allowed' in physics, check if it can be built purely from combinations of kg, m, s, A, K (multiplying or dividing). If it can, it's a valid SI-derived unit.

Trap: Common mix-up: current's SI unit is the ampere (A), not the coulomb (C). The coulomb is the unit of charge, a *derived* quantity (charge = current × time).

Prefixes and standard form

Very large or very small measurements are usually written using prefixes rather than lots of zeros. The ones you need to know: kilo (k, ×10³), centi (c, ×10⁻²), milli (m, ×10⁻³), micro (μ, ×10⁻⁶), and nano (n, ×10⁻⁹).

Scalars vs vectors: a scalar has magnitude only (e.g. mass, distance, speed, time). A vector has both magnitude and direction (e.g. weight, displacement, velocity, force).

Trap: centi (10⁻²) is the odd one out, since most other prefixes step in powers of 1000 (10³). Students sometimes assume 1 m = 100 cm follows the same ×1000 pattern as kilo/milli, it doesn't.

Measuring length: vernier calipers and the micrometer screw gauge

A metre rule measures to the nearest 0.1 cm (1 mm), fine for lengths of a few centimetres or more, but with no way to measure small diameters (e.g. a marble, a wire) accurately.

A vernier caliper measures to a precision of 0.01 cm. Read the main scale up to the vernier scale's zero mark, then find which vernier scale line lines up exactly with a main scale line, that gives the second decimal place.

A micrometer screw gauge measures to a precision of 0.01 mm, for even smaller objects (e.g. wire diameter, sheet thickness). Read the main scale (whole mm and half-mm), then add the thimble scale reading.

Zero error: before you start, check if the instrument reads exactly zero when its jaws/anvil are fully closed. If it doesn't, every reading you take is off by that same fixed amount, and must be corrected using Actual reading = Observed reading − Zero error.

Trap: A **positive** zero error means the instrument already reads *above* zero before you've measured anything, so you subtract it. A **negative** zero error means it reads *below* zero, subtracting a negative number means you actually add it back. Get the sign wrong and every single reading in a whole experiment is affected.

Worked Example

A student uses a micrometer screw gauge to measure the diameter of a wire. Before starting, she closes the jaws with nothing inside and finds the thimble scale reads 0.04 mm past zero. When she then measures the wire, the main scale reads 5.5 mm and the thimble scale reads 0.27 mm.

Why this trips students up: it's tempting to just add the zero error back on 'to be safe', but the correction always follows Actual = Observed − Zero error, whether the zero error itself is positive or negative. Get the sign of the zero error right first, then subtract.

Frequently Asked Questions