What it does
When you read a scale, the thing you are measuring is usually a little way behind the scale marks: the pencil sits beside a ruler that has thickness, the thread of a thermometer is inside the glass, and the water in a measuring cylinder is in the middle of the cylinder while the marks are on the outside. If your eye is not straight in line, your line of sight crosses the scale at the wrong mark. This is parallax error. The page draws each instrument as your eye sees it, with a side view of your eye, the scale and the object. Move the eye slider and the reading shifts, even though nothing has moved. Type what you read and press Check.
It follows the school topics Class 8 Science, exploring the investigative world of science (measuring carefully, reading scales) and Class 9 and Class 11 Physics practical work (least count, errors in measurement). Plan an experiment with the fair test planner, then combine the errors of several readings with the uncertainty propagation calculator.
How to use it
- Choose an instrument: ruler, thermometer or measuring cylinder.
- Leave the eye straight on (0°), read the scale and type your reading. Press Check.
- Move the eye slider to 30° above (or to the right for the ruler) and look again: the pencil end, the thread or the water surface now lines up with a different mark.
- Press New object for a new length, temperature or volume.
- The Level switch (Class 9 and up) adds the least count, the uncertainty of a reading, the parallax error d·tanθ and your percentage error.
Worked example
The water surface in the measuring cylinder is 12 mm behind the scale, and each millilitre takes 1.8 mm of the scale. With your eye 30° above the surface, the line of sight crosses the scale 12 × tan 30° = 12 × 0.577 = 6.93 mm higher, which is 6.93 ÷ 1.8 = 3.85 mL too high. A volume of 46 mL reads as about 50 mL. The ruler is only 3 mm thick and 1 cm is 10 mm long, so at 30° the error is 3 × 0.577 ÷ 10 = 0.17 cm, nearly 2 mm.
A reading is good to about half the smallest division: ± 0.05 cm on a millimetre ruler, ± 0.5 °C on a thermometer marked in degrees, ± 1 mL on a cylinder marked every 2 mL.
Check yourself
Five fresh questions: uncertainty from the least count, percentage error, the size of a parallax shift, where to put your eye for a cylinder, and which way the error goes. Nothing is saved.
Tips
- Always bring your eye level with the mark, or straight above it for a ruler on a table.
- Read a measuring cylinder at the bottom of the curved surface (the meniscus) for water.
- Start a ruler measurement from a clear mark, not a worn end.
FAQ
Why does a thicker gap make it worse? The shift is d·tanθ, so double the gap means double the error at the same angle.
Do digital instruments have parallax error? Not from reading a scale, but they have their own limits, such as the last digit.
Is this from NCERT? No. It is an independent study aid that follows the same school topics, with its own drawings and numbers.
Where the numbers come from
- Parallax error: a sight line at angle θ to the straight-on direction meets a scale d·tanθ away from where it meets an object a distance d behind the scale; least count and reading to half a division; percentage error: standard school measurement.
- Instrument sizes (a 3 mm ruler, a thread 3 mm behind a thermometer scale, a cylinder 24 mm wide with 1.8 mm per mL) are rounded, typical values, made up for the drawing.
- Checked by hand: d·tanθ shifts for each instrument at 0°, 20° and 30°, and the readings the page accepts.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.