How to write a lab report: the sections, what goes in each, and a marked example (a pendulum measures g)

A lab report has a fixed shape: title, abstract, introduction, method, results, discussion, conclusion, references. Each section answers one question a reader has, in order: what did you do and find (abstract), why and what did you expect (introduction), exactly how (method), what came out (results), what it means and how far to trust it (discussion), the one-sentence answer (conclusion). Below, each section is explained with what the marker checks, and a pendulum experiment we made up is written through all eight, numbers included. The lab report is the essay's cousin; the whole essay in order is the other branch of the family.

The eight sections and the question each answers

Section	The reader's question	What the marker checks	Usual length
Title	What is this?	Names the quantity and the method	One line
Abstract	What did you do and find?	Four sentences, the result with its uncertainty	4 sentences
Introduction	Why, and what did you expect?	The formula with its variables; a prediction that is a number	3 short paragraphs
Method	Exactly how?	Repeatable by a stranger; the controlled variables named	Half a page
Results	What came out?	Units in every header; the graph labelled; one calculation in full	A table, a graph, the calculation
Discussion	What does it mean, and how far do I trust it?	A quantitative comparison; an uncertainty with a number; every error with a direction	3 paragraphs
Conclusion	So what is the answer?	Two sentences, nothing new	2 sentences
References	What did you rely on?	The course's style; every looked-up constant	A short list

The names vary. Some courses say Procedure for the method, fold the Analysis into the discussion, or put Purpose and Hypothesis as sub-headings of the introduction. The rubric's names win. What does not vary is the rule that each section answers its question and nothing appears in two.

Where this sits in the courses. The pendulum sits beside two SPH4U ideas by our titles: two-dimensional kinematics and projectile motion, where g is first used as a number, and Newton's law of universal gravitation, where g is explained; the whole map is the SPH4U course map. On the writing side, the Academic Writing course's ideas 16 and 17, academic style: formality, clarity and concision and active and passive voice, are what the method section's voice rests on.

The experiment we will write up

The experiment is invented for this page, and the numbers in it were made up to be realistic and then computed through to the end. A simple pendulum, a small bob on a string, is swung at five string lengths from 0.400 m to 1.200 m. At each length the time for ten swings is measured three times with a stopwatch. The aim is to measure g, the acceleration due to gravity, from the period.

Two pieces of physics, and only two. First, why ten swings and not one: a hand on a stopwatch is late or early by about 0.2 s, and 0.2 s is 10 % of a 2 s period but 1 % of a 20 s run. Timing ten swings divides the reaction-time error by ten. Second, why we plot T² against L rather than T against L. The theory the lab tests is the period formula for a simple pendulum at small angles, T = 2π√(L/g), stated here and not derived (the derivation is first-year physics). T against L is a curve. Squaring both sides gives T² = (4π²/g) × L, a straight line through the origin whose slope is 4π²/g. Make the graph a line and the slope gives g.

Title and abstract

The title names the quantity and the method: Measuring g with a simple pendulum. Not Lab 3, not Pendulum Lab.

The abstract is a four-sentence summary written last, once every number exists. Its four jobs, in order: what was measured, how, the result with its uncertainty, and the comparison with the accepted value. Ours, with the jobs marked in brackets:

The acceleration due to gravity was measured by timing a simple pendulum at five lengths between 0.400 m and 1.200 m [what]. The period squared was plotted against length and g was found from the slope [how]. The result, 9.80 ± 0.2 m/s², agrees with the accepted 9.81 m/s² within the uncertainty [result and comparison]. Timing by hand was the largest source of uncertainty [the one limit].

Introduction: purpose, theory, hypothesis

Three short paragraphs.

Purpose. One sentence: This experiment measures g from the period of a simple pendulum at five lengths.

Theory. The formula, every variable defined, and the linearisation (the step that turns the curve into a line) stated: For small swings the period T of a simple pendulum of length L is T = 2π√(L/g), where g is the acceleration due to gravity. Squaring gives T² = (4π²/g) L, so a graph of T² against L is a straight line through the origin with slope 4π²/g.

Prediction. A number, not a feeling. 4π² = 39.48, and 39.48 ÷ 9.81 = 4.02, so: If g is 9.81 m/s², the graph will be a straight line through the origin with slope 4.02 s²/m. The marker checks that the formula is there with its variables defined and that the prediction is a number or a shape that could turn out wrong. g will be about 9.8 is not a prediction; the slope is.

Method: enough for someone else to repeat it

Past tense, and the passive is accepted here: The string was measured from the pivot to the centre of the bob. The reader does not care who held the metre stick; the string is the topic. When the passive is the right choice explains why this is the one section where it is. Numbered steps or a paragraph, either is fine; the rubric decides.

What goes in: the equipment with its precision (a metre stick reading to 0.001 m; a stopwatch reading to 0.01 s but a hand that starts and stops it to about 0.2 s), the controlled variables (the same bob throughout; the amplitude, the size of the swing, kept under 15°, because the small-angle formula fails for wide swings), how the length was measured (pivot to the centre of the bob), how the count was started (at the centre of the swing, where the bob moves fastest and the moment is sharpest), and how many trials (three runs of ten swings at each of five lengths).

The marker's two checks: could they repeat it without asking you anything, and is the thing you held constant named.

Results: the table, the graph, the calculation

The data table, every number computed on the page. The three runs are the raw times for ten swings; the mean is their average; T is the mean divided by ten; T² is T squared.

L (m)	Ten swings, run 1 (s)	Run 2 (s)	Run 3 (s)	Mean (s)	T (s)	T² (s²)
0.400	12.7	12.6	12.8	12.70	1.270	1.613
0.600	15.6	15.5	15.6	15.57	1.557	2.423
0.800	17.9	18.0	18.0	17.97	1.797	3.228
1.000	20.1	20.0	20.1	20.07	2.007	4.027
1.200	22.0	22.1	21.9	22.00	2.200	4.840

One row in full, so the reader can check the rest: at L = 0.400 m the mean is (12.7 + 12.6 + 12.8) ÷ 3 = 38.1 ÷ 3 = 12.70 s; T = 12.70 ÷ 10 = 1.270 s; T² = 1.270 × 1.270 = 1.613 s².

The graph, described: T² on the vertical axis in s², L on the horizontal in m, five points, a line of best fit. A least-squares fit through the five points gives a slope of 4.029 s²/m and an intercept of 0.003 s², which is zero to two decimals: the line passes through the origin as the theory said. Rounded to the three significant figures the data support, the slope is 4.03 s²/m. If you fit the line by eye with a ruler, say so in the report; you should get about 4.0 s²/m.

The calculation, shown once in full:

g = 4π² ÷ slope = 39.48 ÷ 4.03 = 9.80 m/s².

A check from one point, so the reader sees the slope method and the single-length method agree: at L = 1.000 m alone, g = 4π² L ÷ T² = 39.48 × 1.000 ÷ 4.027 = 9.80 m/s².

The marker's checks: units in every column header; a consistent number of significant figures (three for the lengths and for g, four where the timing supports it); the graph with both axes labelled and the slope stated; the calculation written out once, not five times.

Discussion: what it means and how far to trust it

Three jobs, three paragraphs.

The comparison. Percent difference = |accepted − measured| ÷ accepted × 100 % = |9.81 − 9.80| ÷ 9.81 × 100 % = 0.01 ÷ 9.81 × 100 % = 0.1 %. Write the formula, the numbers and the result.

The uncertainty. A hand-timing uncertainty of 0.2 s on a run of about 20 s is 1 % in the time, and squaring a quantity doubles its relative uncertainty, so about 2 % in T². The length was read to 0.002 m on a metre of string, about 0.2 %. Relative uncertainties add, so about 2 % in g, and 2 % of 9.80 m/s² is 0.2 m/s². The result is 9.80 ± 0.2 m/s², and the accepted 9.81 lies inside it. That sentence, not the 0.1 %, is the one that says the experiment worked. (The rule used here, relative uncertainties add and a square doubles one, is the first rule of Taylor's error analysis text; a Grade 12 report needs no more than that.)

The sources of error, each with its direction. An amplitude over about 15° lengthens the period, which makes T² larger and g smaller. Measuring L to the top of the bob instead of its centre makes L too short, which also lowers g. Starting the count at an extreme of the swing rather than the centre adds a random error to the time. The string stretches a little at the longest length, which makes the true L larger than the measured one and lowers the measured g.

The honest paragraph. Human error is not a source of error, and a marker strikes it out. It names nobody and points nowhere. Name the measurement (hand timing), its size (about 0.2 s), and which way it pushes the result (either way, which is why it appears as the uncertainty rather than as a bias). The marker checks three things in this section: the comparison is quantitative, the uncertainty has a number, and every error source has a direction.

Conclusion: the one-sentence answer

Two sentences, nothing new. Ours: The acceleration due to gravity measured from the pendulum's period was 9.80 ± 0.2 m/s², which agrees with the accepted value of 9.81 m/s² within the uncertainty. Hand timing set the uncertainty; a photogate would reduce it.

For the reader for whom discussion and conclusion sound the same: the discussion argues (compares, estimates, names causes); the conclusion states. If a sentence in your conclusion would need a reason, it belongs in the discussion.

References

The course textbook and any data source, in the style the course asks for; the sciences usually ask for APA, and the APA reference entry shows the shape. The accepted value of g needs no citation when the course gives it. A constant you looked up does.

The marker's checklist, all eight sections

Run it on your own report before you hand it in. Then find the one line in the calculation that moved the answer most and check that line twice; that is chapter 4 of the free playbook.

1. Title: names the quantity and the method, not the lab number.
2. Abstract: four sentences, the result with its uncertainty, written last.
3. Introduction: the formula with every variable defined, and a prediction that is a number or a shape.
4. Method: someone else could repeat it; the controlled variables named; the instruments with their precision.
5. Results: units in every header, consistent significant figures, the graph labelled, one calculation shown in full.
6. Discussion: a quantitative comparison, an uncertainty with a number, every error source with a direction, no "human error".
7. Conclusion: two sentences, the result and whether it agrees, nothing new.
8. References: the course's style, every looked-up constant and the textbook cited.

The report is one genre of the sciences' writing; how to study the sciences has the routine around it, and the theory behind the restoring force that makes a pendulum swing is free-body diagrams and Newton's laws.

The lab report on one screen

• Title: what is this? The quantity and the method.
• Abstract: what did you do and find? Four sentences, written last.
• Introduction: why, and what did you expect? The formula and a numerical prediction.
• Method: exactly how? Repeatable, past tense, the controlled variables named.
• Results: what came out? Table, graph, one calculation in full.
• Discussion: what does it mean, and how far do I trust it? Comparison, uncertainty, errors with directions.
• Conclusion: so what is the answer? Two sentences.
• References: what did you rely on? The course's style.