Reading an analogue scale means finding the value of one small division, reading the nearest mark, and then estimating any fraction between marks. It appears whenever you use a ruler, thermometer, measuring cylinder, ammeter or voltmeter in measurement and quantities.
The step most students skip is working out what each small division is worth. Labels on a scale are usually spaced further apart than the marks.
How do I read any scale, step by step?
- Find the value of one small division. Take two labelled marks, subtract, and divide by the number of spaces between them.
- Start from the last labelled mark the pointer has passed.
- Count the small divisions beyond it and multiply by the division value.
- Estimate between marks. Decide if the pointer is nearer the lower mark, halfway, or nearer the upper mark.
- Write the reading with its unit, to a sensible number of decimal places.
Read with your eye level with the pointer. Looking from the side makes the pointer seem to sit against a different mark, which is called parallax.
Worked example
A voltmeter scale is labelled 0, 2, 4, 6, 8, 10 V. There are four equal spaces between each pair of labelled marks. The pointer is past the 4 V label, three small divisions further, and a little past the third mark. (Invented example data.)
Step 1, value of a small division: (6 − 4) ÷ 4 = 0.5 V per division.
Step 2, last labelled mark passed: 4 V.
Step 3, count divisions: three divisions × 0.5 V = 1.5 V, so the third mark reads 4 + 1.5 = 5.5 V.
Step 4, estimate between marks: the pointer is a little past 5.5 V, about a fifth of the way to 6.0 V. A fifth of 0.5 V is 0.1 V, so the reading is about 5.6 V.
Answer: about 5.6 V, and 5.5 V or 5.7 V would show a reasonable judgement of the pointer position.
The mistake to watch for
A common slip is to count each small division as 1, because the eye sees “four marks past the label, so add four”.
Mistaken answer: 4 + 3 = 7 V
The student counted marks instead of using the value of each division.
The correction is always to work out the division value first. Here a reading of 7 V would place the pointer beyond the 6 V label, which the picture clearly shows it has not reached. Comparing your answer with the nearest labelled marks is a quick plausibility check.
A second slip is forgetting that an object may not start at zero. If a ruler is used with one end of the object at 2.0 cm, subtract the start reading from the end reading.
Check yourself
1. A thermometer is labelled every 10 °C. There are ten equal spaces between labels. The liquid is three small divisions above the 30 °C label. What is the temperature?
Show answer
One small division = 10 ÷ 10 = 1 °C. Reading = 30 + 3 = 33 °C.
2. A scale is labelled 0, 5, 10, with five equal spaces between each label. The pointer is exactly on the second mark after 5. What is the reading?
Show answer
One small division = 5 ÷ 5 = 1 unit. Reading = 5 + 2 = 7 units.
3. One end of a rod is at 3.0 cm on a ruler and the other end is at 8.4 cm. What is the length of the rod?
Show answer
Length = 8.4 − 3.0 = 5.4 cm.
Where this leads next
Once single readings are dependable, learn to combine several of them in calculating a repeated-measurement mean. A good earlier step is choosing a unit appropriate to a quantity, and the measurement and quantities practice set mixes both skills. The bounds and rounding explainer shows how reading precision limits your answer.
If you can read the scale in class but freeze under exam timing, our teachers can practise with you in online one-to-one Physics tuition.