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You meet Hooke's law as one line, F = kx, and usually as a definition. But it started as an experimental claim that a 17th-century scientist tested with wire, weights and wood, and the original lecture has more physics in it than most textbooks show. This post reads what Robert Hooke actually wrote, works through his experiment with modern numbers, and shows how his own arithmetic leads to the spring-energy formula.
Who was Robert Hooke?
The University of California Museum of Paleontology's biography gives his dates as 1635 to 1703 and calls him perhaps the single greatest experimental scientist of the 17th century. Among his inventions it lists the anchor escapement and the balance spring, which made more accurate clocks possible. He served as Chief Surveyor and helped rebuild London after the Great Fire of 1666, and he devised the equation for elasticity still used as Hooke's law. His microscope work is a separate story, told in our post on Hooke's Micrographia and the first use of the word cell.
How did Hooke announce the law?
In 1678 Hooke published Lectures de Potentia Restitutiva, or of Spring, now scanned in full on the Internet Archive. He wrote that about two years earlier he had printed the theory as an anagram, a scrambled string of letters, at the end of a book describing helioscopes. The letters unscramble to "Ut tensio sic vis", Latin for "as the extension, so the force".
He then gave it in English. In modern spelling: "The Power of any Spring is in the same proportion with the Tension thereof". In other words, one weight stretches the spring one space, two weights stretch it two, three stretch it three, and so on. He also wrote that about three years before, the King had seen the experiment at Whitehall, together with his spring watch.
How did he test it?
The lecture describes the method. Take evenly drawn wire of steel, iron or brass, coil it on a cylinder into a helix, and turn both ends into loops. Hang the coil from a nail, hang a small scale pan from the other end, and add weights. Hooke used weights in the proportion 1, 2, 3 and so on up to 8, and found the spring stretched by equal steps. He described the same behaviour in a piece of dry wood clamped at one end and loaded at the other.
That habit, testing one claim on several materials, is why he felt able to call it a rule for "any Spring".
Worked example 1: from Hooke's experiment to a spring constant
Suppose a coil stretches 2.0 cm when you hang a 0.50 kg mass from it. Take g = 9.8 m/s².
Step 1: force. F = mg = 0.50 × 9.8 = 4.9 N.
Step 2: spring constant. k = F/x = 4.9 ÷ 0.020 = 245 N/m.
Step 3: predict. With 1.5 kg, F = 14.7 N, so x = 14.7 ÷ 245 = 0.060 m = 6.0 cm. Three times the weight, three times the stretch, exactly Hooke's "three will bend it three".
Worked example 2: Hooke's 1-3-5-7 rule and ½kx²
Later in the lecture Hooke made a second, subtler point. Every point along the stretch has its own force, starting from nothing. Added together, he wrote, these forces are in "duplicate proportion" to the stretch, meaning they grow as its square. So the totals for one, two and three spaces are as 1, 4 and 9, and the amounts added in each successive space are as 1, 3, 5, 7.
In modern terms that total is the work done, the area under the F-x line: U = ½kx². Check with the spring above, in 2 cm steps:
At 2 cm: U = ½ × 245 × (0.02)² = 0.049 J.
At 4 cm: U = ½ × 245 × (0.04)² = 0.196 J.
At 6 cm: U = ½ × 245 × (0.06)² = 0.441 J.
The increments are 0.049, 0.147 and 0.245 J, in the ratio 1 : 3 : 5, just as Hooke wrote. Our post on spring-block energy problems uses the same result.
Where does Hooke's law stop working?
Hooke said "any Spring", but the modern view is more careful. NCERT's Class 11 chapter on mechanical properties of solids states that stress is proportional to strain only for small deformations, calls Hooke's law an empirical law valid for most materials, and shows that on a stress-strain curve it holds only in the initial straight region. It also notes that a class of solids called elastomers, such as rubber, does not obey it. Hooke's law, stress-strain relationship and Young's modulus are listed in Unit 7 of the JEE (Main) 2026 syllabus.
What mistakes do students make with springs?
Using mass for force. k = mg/x, not m/x.
Leaving extension in centimetres. Convert 2.0 cm to 0.020 m before dividing.
Dropping the sign. The spring's force opposes the stretch, F = −kx, which matters in oscillation problems.
Assuming energy grows like force. It grows with x², as worked example 2 shows.
Applying the law beyond the elastic limit. Past the straight region, the formula no longer holds.
What can a student take from Hooke's way of working?
Hooke did not stop at one coil. He tried different metals and wood, then pushed the idea further by asking what the forces add up to. Test a rule in several cases, and then ask what follows from it.
If you want to see the force and energy graphs change as a spring stretches, the Fermi Simulation Lab has interactive simulations for ideas easier to see than read.
Hang three equal weights one by one from a spring and a rubber band, measure each stretch with a ruler, and plot both: you will see where Hooke's law holds and where it breaks.
