The elastic force is the spring constant times the extension: Fv = C × u. The extension u is the difference in length between the stretched and the unstretched spring, in metres. The spring constant C is the force needed to stretch the spring by one metre, in newtons per metre. The bigger C, the stiffer the spring.
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A spring of ten centimetres becomes fourteen centimetres with one small weight on it. Hang two on it and it becomes eighteen centimetres, not twenty-eight. What doubles is not the length of the spring.
What doubles is the extension: the difference in length between the stretched and the unstretched spring, with the letter u. How far a spring stretches also depends on the spring itself. That is in the spring constant C: the force needed to stretch the spring by one metre. A stiff spring has a big spring constant, a soft one a small one. The elastic force is then Fv = C × u, with the elastic force in newtons, the spring constant in newtons per metre and the extension in metres. You work out two springs that stretch three and twelve centimetres at 6 N: 200 N/m and 50 N/m. And you calculate the mass of a small plant on a spring of 40 N/m that stretches twelve centimetres: 4.8 N, so 0.49 kg.
For high school physics, in the chapter on forces. Halfway through there is a question and a pause: stop the video there and think for yourself first.
In this video
The full explanation, in writing
Two small weights
0:00A spring of ten centimetres. You hang one small weight on it, and it becomes fourteen centimetres. Now you hang two on it. How long is it then?
What doubles
0:15Eighteen centimetres. What doubles is not the length of the spring, but the piece that is added: the extension. The extension is the difference in length between the stretched spring and the unstretched spring, and it gets the letter u. With one small weight this spring stretches four centimetres, from ten to fourteen.
0:37With two small weights it stretches twice as far, eight centimetres, and then it is eighteen centimetres long.
Stiff or soft
0:45How far a spring stretches also depends on the spring itself, and that is in the spring constant. The spring constant C is the force needed to stretch the spring by one metre. A stiff spring, with the same force, stretches a little, a soft one a lot.
1:02The bigger the spring constant, the stiffer the spring. The elastic force is then F v is C times u: the elastic force in newtons, the spring constant in newtons per metre, and the extension in metres. Your turn. Two springs, both with a force of six newtons on them.
1:20One stretches three centimetres, the other twelve. Which has the bigger spring constant?
A plant on a spring
1:31The spring that stretches three centimetres: it is the stiffest. To work it out, first convert the centimetres to metres. Six divided by zero point zero three zero is two hundred newtons per metre. For the other it is six divided by zero point one two: fifty newtons per metre.
1:49One more. A spring with a spring constant of forty newtons per metre stretches twelve centimetres when you hang a small plant on it. Twelve centimetres is zero point one two metres. The elastic force is forty times zero point one two: four point eight newtons.
2:07If the plant hangs still, the elastic force is just as big as the force of gravity on the plant. So the mass is four point eight divided by nine point eight one: zero point four nine kilograms.
Three things to remember
2:20Three things. The extension is the difference in length between the stretched and the unstretched spring, not the length of the spring. The spring constant is the force needed to stretch the spring by one metre: the bigger, the stiffer. And the elastic force is C times u, with u in metres.
Two questions
2:42Two questions. One. A spring with a spring constant of two hundred newtons per metre stretches five point zero centimetres. How big is the elastic force? Two. A spring is twenty centimetres long. With a small weight on it, it is twenty-four centimetres.
2:58You hang three times as much on it. How long does it become?
The answers
3:05The first: five point zero centimetres is zero point zero five zero metres. Two hundred times zero point zero five zero is ten newtons. The second: the extension was four centimetres, and three times as much weight gives three times as much extension: twelve centimetres.
3:23The spring becomes twenty plus twelve is thirty-two centimetres.
Directly proportional
3:27Do you want to know how to show that two quantities are directly proportional? Then watch the video about directly proportional relationships on my YouTube channel.
Frequently asked questions
What is the extension of a spring?
The extension u is the difference in length between the stretched and the unstretched spring, not the length of the spring itself. A 10 cm spring that becomes 14 cm long has an extension of 4 cm.
What is the spring constant?
The spring constant C is the force needed to stretch the spring by one metre, in newtons per metre. The bigger the spring constant, the stiffer the spring: with the same force, a stiff spring stretches less far than a soft one.
How do you calculate the spring constant?
Divide the elastic force by the extension in metres: C = Fv / u. A spring that stretches 3.0 cm at 6 N: 6 / 0.030 = 200 N/m. So convert the centimetres to metres first.
How do you calculate the elastic force?
With Fv = C × u. A spring of 200 N/m that stretches 5.0 cm: 5.0 cm is 0.050 m, and 200 × 0.050 = 10 N.
How long does a spring become if you hang three times as much weight on it?
The extension becomes three times as big, not the length. A 20 cm spring that is 24 cm with one small weight stretches 4 cm. With three times as much weight it stretches 12 cm and becomes 32 cm.
The elastic force is the spring constant times the extension, with the extension in metres.
Physics with Thomas makes physics explainers for secondary school. No words on screen, so what you see works in any language.
In this series
Types of forces3:06
Calculating gravity3:15
Centre of gravity2:48
Force meter: range and precision3:11
Elastic force and spring constant3:41
Directly proportional relationship3:37
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.