Stepping Science: Estimating Somebody’s Height from Their Walk
Summary
Introduction
Have you ever noticed you need to walk faster just to keep up with some people, or decrease your pace to walk with other people who are going slower? This is likely because of the difference in leg length between you and the person you are walking with. In this science activity, you’ll get to investigate just how much faster or slower different people walk, and see if you can use the relationship between a person’s walking pace and their height to estimate your own height.
Background
A pedometer is an instrument that is often used by joggers and walkers to tell them how far a distance they have gone. On some pedometers, when a person sets the instrument before an outing, they must enter their height into the pedometer to get an accurate reading.
Materials
- 20 feet of straight sidewalk or a long, straight hallway
- Sidewalk chalk or two small objects to mark off 20 feet of distance
- Tape measure
- At least three volunteers to walk a short distance. They should ideally have different heights.
- Pen or pencil
- Scrap piece of paper
- Calculator
Preparation
- Find a place that has 20 feet (ft.) of straight sidewalk or find a straight hallway that is at least 20 ft. long.
- Using a tape measure, measure out a distance of 20 ft. and mark the beginning and ending points with a piece of sidewalk chalk (if you are using a sidewalk), or mark them each with a small object that will not be moved (if you are using an indoor hallway).
Instructions
- Measure a volunteer’s height. How tall are they? Write their height down on a scrap piece of paper.
- Ask the volunteer to walk from the beginning to the end of the 20 foot course you marked while counting the number of steps they take. How many steps did they take? Write down the answer.
- Repeat this process for at least two more volunteers. How tall is each volunteer? Did they take a similar number of steps, or was there variation? Be sure to write the results down.
- For each volunteer, figure out their step length (in feet) by dividing 20 ft. by the number of steps each took. What was the step length for each volunteer?
- For each volunteer, figure out their ratio of step length to height by dividing their step length by their height (both in feet). What numbers do you get for this ratio? Are they similar for the different volunteers, or is there variation? Average the step length to height ratio for all of your volunteers. Be sure to write your answers down.
- Lastly use your results to estimate your own height. Walk from one end to the other of your 20 foot course while counting the number of steps you take. Divide 20 ft. by the number of steps you took. What was your step length? Then divide your step length by the volunteers’ average ratio of step length to height. Based on your data, what is your estimated height?
- Have someone measure your actual height. How does your actual height compare to your estimated height? How accurate was your estimate?
Extra: Try this activity with a greater number of people. For example, you could go to a park with a jogging path or a similar location where you can ask for volunteers as they pass by. Try to collect data from at least 10 volunteers. Is there much variation in the ratio of step length to height when comparing many people? Does collecting more data make your height estimation more accurate?
Extra: You could do this activity again but this time have volunteers walk slowly, moderately fast or very fast. How does a person’s speed affect their step length?
Extra: The human body has many other interesting ratios, such as mentioned in the Background of this activity. You could look into other ratios in the human body and come up with an activity like this one to investigate them. See the More to Explore section on the next page for relevant resources. What other ratios are consistently found in the human body from person to person?
Observations and Results
When you divided your volunteers’ step length by their height, did you get a ratio value close to 0.4? Were you able to roughly estimate your height based on this, accurate to within two inches?
The measurements of a pedometer are based on the hypothesis that all people have common ratios and proportions, even if they are different heights. In this activity you should have found this hypothesis to be pretty accurate. On average, people have a step length of about 2.2 to 2.5 feet. In general, if you divide a person’s step length by their height, the ratio value you get is about 0.4 (with a range from about 0.41 to 0.45). This is why you can take a person’s step length and divide it by about 0.43 to roughly estimate their height – the estimated height will likely be within two inches of (and probably much closer to) their actual height.
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Additional Resources
- Pedometers for Kids Track Physical Activity, from Peaceful Playgrounds
- Simple Ratios of the Human Body, from Kim Moldofsky at Bedtime Math
- How to Determine Stride for a Pedometer by Height & Weight, from Amy Sutton at the Houston Chronicle
- Keeping Up, from Science Buddies
