Measuring Instruments for School Labs
A measuring instrument is a device used to determine the value of a physical quantity, and the common instruments in a school laboratory are the ruler, balance, stopwatch, thermometer and graduated cylinder, each with a limited scale resolution that determines the smallest difference it can show. In brief: the reading uncertainty of an instrument is often taken as half of the smallest scale division for analog instruments, and as the last digit for digital ones. Correct technique, such as reading at eye level and checking for zero error, is as important as the instrument itself.
Almost every experiment in physics starts with a measurement, and the quality of the result depends on the choice and use of the instrument. This guide describes the main instruments for length, mass, time, temperature and volume, explains how to read scales and choose the right instrument, compares them in a table, works through a reading example and corrects common mistakes.
What should you know about measuring instruments?
- Range: the smallest and largest values that the instrument can measure.
- Resolution (scale division): the smallest change that can be read. A ruler marked in millimeters has a resolution of 1 mm.
- Zero error: a nonzero reading when the true value is zero. It is checked before the measurement and subtracted.
- Analog or digital: analog instruments have a scale and pointer, and digital ones show a number.
- Parallax error: an apparent shift in the reading when the scale is viewed from an angle. The eye should be directly in front of the mark.
How are lengths measured?
A ruler (usually 30 cm, with millimeter marks) is used for lengths of a few centimeters to decimeters. The object should be placed against the scale with one end at a clear mark, such as 1 cm instead of the worn end of the ruler, to avoid an end error. A measuring tape is flexible, and is used for longer distances or curved lines, and a trundle wheel for long distances outdoors. For more precision, the vernier caliper (typically 0.1 mm or 0.05 mm) and micrometer screw gauge (0.01 mm) are used.
How is mass measured?
A balance compares the mass of an object with known masses (beam balance) or measures the force on a sensor and converts it to mass (electronic balance). Before use, it is placed on a level surface, and set to zero (tared). Electronic balances in schools typically read to 0.1 g or 0.01 g. An electronic balance actually measures the force, so its calibration depends on gravity at the location. A spring scale (newton meter) measures the weight in newtons, not mass.
How is time measured?
A stopwatch measures time intervals, usually to 0.01 s, but the human reaction time of about 0.2 s is the main source of uncertainty when it is started and stopped by hand. To reduce the effect, a long time interval can be measured (the time for 20 oscillations of a pendulum, then divided by 20) and the measurement can be repeated. Electronic timers and light gates reduce the reaction-time problem. A clock or a watch shows the time of day.
How is temperature measured?
A liquid-in-glass thermometer uses the expansion of colored alcohol or mercury in a narrow tube, and school thermometers usually read from −10 °C to 110 °C with 1 °C divisions. The bulb must be in the liquid and not touching the container, and the reading should be taken after the level has stopped changing. Digital thermometers use a thermistor or thermocouple and show the value to 0.1 °C.
How is volume of a liquid measured?
A graduated (measuring) cylinder measures the volume of liquids. Water forms a curved surface (the meniscus) in the glass, and the reading is taken at the bottom of the curve, with the eye at the same level. Cylinders are placed on a flat surface. A narrow cylinder gives a more precise reading than a wide one of the same capacity. For irregular solids, the volume can be found from the rise of water level when the solid is immersed (displacement method). Other glassware includes beakers (approximate), pipettes and burettes (more accurate).
Instruments compared
| Quantity | Instrument | Typical resolution | Main source of error |
|---|---|---|---|
| Length | Ruler (30 cm) | 1 mm | Parallax, end error |
| Length (small) | Vernier caliper | 0.1 mm | Zero error |
| Mass | Electronic balance | 0.01 g | Not tared, uneven surface |
| Time | Stopwatch | 0.01 s | Reaction time |
| Temperature | Liquid thermometer | 1 °C | Reading too soon, bulb touching the glass |
| Volume | Graduated cylinder (100 mL) | 1 mL | Meniscus, parallax |
Worked example: reading scales
A student measures a wooden block with a ruler marked in millimeters, a liquid with a 100 mL graduated cylinder marked every 1 mL, and the time of 20 swings of a pendulum with a stopwatch.
- Ruler: the block starts at the 1.0 cm mark and ends at 8.4 cm. Length = 8.4 − 1.0 = 7.4 cm. The reading uncertainty is half of the smallest division, 0.5 mm = 0.05 cm, but it applies to both ends, so a practical uncertainty of ±0.1 cm is reasonable. Result: (7.4 ± 0.1) cm.
- Cylinder: the bottom of the meniscus is at 63 mL. With divisions of 1 mL, the reading is (63.0 ± 0.5) mL.
- Pendulum: 20 swings take 31.4 s. The period is 31.4 ÷ 20 = 1.57 s. If the reaction-time uncertainty is ±0.2 s for the whole measurement, the uncertainty in the period is 0.2 ÷ 20 = ±0.01 s. Result: (1.57 ± 0.01) s.
The last step illustrates why timing many oscillations improves precision: the same absolute uncertainty is divided by the number of oscillations.
How did instruments develop?
Galileo built an early thermoscope around 1600, and Daniel Fahrenheit made reliable mercury thermometers in 1714. The vernier scale was described by Pierre Vernier in 1631. Christiaan Huygens made the first pendulum clock in 1656. Electronic balances became common in laboratories in the second half of the twentieth century, and digital instruments with sensors and data loggers are now widely used in teaching.
Which mistakes are common?
Mistake 1: Reading the scale from an angle
Parallax produces systematic errors. Place the eye level with the mark.
Mistake 2: Ignoring the zero error
Check the zero before measuring, and correct the result if it is not zero.
Mistake 3: Reading the top of the meniscus
For water, the reading is taken at the bottom of the curved surface.
Mistake 4: Giving more digits than the instrument allows
The result cannot be more precise than the resolution of the instrument. A ruler marked in millimeters gives a length to the nearest millimeter, or a half of it at best.