Estimating Physical Quantities
Estimating Physical Quantities
- Some exam questions ask for a reasonable estimate of an everyday quantity. No measuring is possible; you must build the answer from values you already know.
- An estimate only needs the right power of ten, not a precise value.
? m s⁻¹? cm³? AValues to remember
- Memorise a few standard values. Almost every estimate question is built from them.
| Everyday quantity | Value to remember |
|---|---|
| mass of an adult | 70 kg |
| height of an adult | 1.7 m |
| walking speed | 1 m s⁻¹ |
| motorway car speed | 30 m s⁻¹ |
| density of water | 1000 kg m⁻³ |
| g (free-fall acceleration) | 9.81 m s⁻² (≈ 10) |
| weight of an apple | ≈ 1 N |
| thickness of a sheet of paper | ≈ 0.1 mm |
Making an estimate
- Pick the standard values the quantity needs.
- Combine them with a simple formula (weight = , mass = density × volume, volume = length × width × height).
- Round to one figure and compare powers of ten.
Worked example
Smallest case: the weight of an adult
Choose the best estimate: 7×10⁰, 7×10², 7×10⁴ or 7×10⁶ N.
- Take the mass of an adult: .
- Weight is a force: .
- Nearest choice: .
Answer
(9702/12/O/N/25 Q1)
Your turn— tap to reveal the worked answer (9702/11/O/N/24 Q4)
Give a reasonable estimate of the volume of one page of an exam paper, in mm³. (9702/11/O/N/24 Q4)
- A page is about 300 mm long and 210 mm wide. Paper is about 0.1 mm thick.
- Volume: .
Answer: about 6000 mm³. Only the power of ten needs to be right.
Estimation only needs the right power of ten. Start from values you know, combine them, and round to one figure.
Common mistake
Estimating the wrong quantity. Weight is in newtons, so multiply the mass by . Writing 70 N (forgetting ) or 700 kg (a mass, not a weight) is wrong either way.