When I was in high school, we measured Earth’s gravity. This number is known as “g”, or sometimes “little g” to distinguish it from “big G” which is something else.
This is an acceleration, or the rate of change of speed over time. The number is in units of meters-per-second-per-second, which means starting from rest and going at a constant acceleration, after one second you’ll be going at some number of meters-per-second. Another second after that you’ll be going twice as fast.
Have you ever wanted to measure Earth’s gravity for yourself? You can do it with nothing more than a tennis ball, a stopwatch, a long tape measure and somewhere to stand.
When in doubt, drop something.
First, find a high platform that you can safely drop a tennis ball from that has a floor at the bottom which makes an audible bounce. At school, we used a three‑floor open stairwell. Once you’ve chosen your spot, measure the height from your release point to the ground using the tape measure.
Now comes the timing. Hold the tennis ball in one hand and the stopwatch in the other. Drop the ball — don’t throw it — and time how long it takes from the moment you let go to the moment you hear it hit the ground. Repeat this several times and record the time taken each time.
Starting the stopwatch as you release the ball is something you can do with a little practice, but stopping the stopwatch at the right moment is trickier. The main factor causing a problem is the quite mundane human reaction time.
Think about what happens. The sound waves of the bounce enters your ears. Impulses travel from your ear to your brain. Your brain says “That was a bounce. I need to stop the stopwatch.” Your brain sends another signal to your fingers to press the button. The muscles in your hand pull your fingers to finally stop the stopwatch.
That process takes a small amount of time but will be enough to throw off your measurements. What you want is a consistent reaction that you can treat as a fixed delay in your timing. Before you set out, you can have a friend bounce your tennis ball on the floor behind you and measure how long it takes from bounce to click. With practice you can get that all‑important consistent reaction time. (Remember that consistency is more important here than being fast, unless maybe you’re a test pilot.) If you don’t subtract a reaction‑time estimate, your measured will come out a bit low but still recognisably “about 9.8”.
Some stopwatch readings will inevitably be off. Perhaps you hesitated on the stopwatch or nudged the ball slightly as you released it. Once you have a few readings, look for the median. This is the one reading that has an equal number of bigger readings as smaller readings. By ignoring those occasional outliers, you get the most reliable reading of the true fall time.
Let the numbers speak for themselves.
With your measured height and your median fall time, you can now calculate the acceleration due to gravity. The height you’d expect a falling object to travel is given by the following formula:
Let’s quickly pull that apart. The height (h) is equal to half the acceleration due to gravity (g) multiplied by the square of the time (t). The ½ appears because the ball starts from rest and its speed increases steadily, so the average speed during the fall will be half of the final speed. The time is squared because the ball is accelerating constantly. The more time the ball has to fall, the faster it is going to get, which boils down to being proportional to the square of the time. That formula will tell us how far something should fall in a given time, but since we already know the height we can rearrange it to solve for that gravity factor, g, instead.
Plug the height (h) and the time (t) into this rearranged formula and your value for g pops out! Congratulations, you’ve measured the acceleration of Earth’s gravity! Get yourself a drink to celebrate.
When we did this in school, our measurements came out at about 8.7 m/s². This was not quite the official 9.8 m/s², but impressively close for a bunch of spotty teenagers!
Calculated g: —
Nullius in verba...
I present this in the spirit of do-it-yourself. My hope is that you do actually grab the equipment that you might already have lying around, find a suitable height and actually do this measurement. You don’t need a lab coat or a particle accelerator, just some random sports equipment and a bit of curiosity. It is a great feeling to be able to say you personally measured Earth's gravity yourself. You could have looked it up in a book, but you're not the type to just take someone's word for it, no no no!
But in this spirit, we should discuss a few compromises we had to make along the way.
The time between hearing the bounce and stopping the stopwatch also includes the time taken for the sound of the bounce to travel back up to you at the speed of sound. As well as this, air resistance will slow the ball's journey a little. Don't worry about these because they're tiny compared to unavoidable human reaction time.
If you are chasing precision, going beyond a little bit of fun, those bits of uncontrolled noise do matter a lot. Throw away the stopwatch and get some precision timing equipment and perform the drop in a vacuum chamber instead.
Also, we've rather glibly assumed that gravity is a constant acceleration. If you don't want to be making assumptions about the nature of gravity, repeat the measurement at a variety of different heights. You should get the same result for g regardless of what height you dropped the ball from.
If you do get a different g with height, it will be very possible you've discovered a new property of gravity that science doesn't know about. They'll name this new side of gravity after you and people will list your name alongside Newton and Einstein. But just in case, it may be more likely something is off with your setup, so check your precision timing equipment is working before calling the science journals.
Credits
📸 "Moss Landing Otter" by Jim Bahn. (Creative Commons)
📸 "Clanger - The Beaney" by Peter Taylor. (Creative Commons)
🤖 Thanks to Microsoft Copilot for checking my science.