Smartphones have continued to increase in size, but our hands have not.
Have you ever wondered how big your hands would need to be to easily reach the entire screen only using one hand? The answer: Your hands would need to be as big as those of a professional football and basketball. Read about our calculations and sources below.
We also calculated how far the average man and woman can reach on four popular smartphone models: The iPhone 6, 6 Plus, Samsung Galaxy S5, and Galaxy Note 4. Be sure to check out how your hand compares with our two printouts as well.
Follow the links below for printer-friendly pdf versions of how large your hand needs to be to reach the entire screen of an iPhone 6 and a Samsung Galaxy S5.
This project aimed to estimate how much of the phone your right hand can reach using a “shelf grip” approach. Previous studies did not make any attempt to quantify how much of the screen people could reach, but rather took a subjective approach based on how a phone felt in one’s hands. Their “thumb zone” consisted of a sweeping arc from the bottom left corner to almost the middle-right of the phone.
Determining formulas to calculate their precise area was beyond the scope of this project. Rather, this project assumed thumb motion occurs in a radial fashion. We were able to perform our calculations using the Pythagorean Theorem, which states:
a2 + b2 = c2
We used a fixed location for the thumb, with the center along the right side of the phone, 1/4 the distance from the bottom. This fixed location was necessary for our calculations, when in reality people shift their grip while using their phone. The shelf grip is limited by physiology, and has an unreachable zone from half of the phone’s width on the bottom to 1/4 of the phone’s height on the right.
We estimated the base of your thumb is 1/4 the width of your hand above the phone. Assuming a 90 degree angle between the phone and your hand, we then used Pythagorean’s Theorem to figure out how far your thumb could “easily” reach, using the thumb length as the hypotenuse of the triangle.
To recap, 1/4 the width of the hand is one of the sides of the triangle, side b, the thumb length is the hypotenuse, c, and the green, “natural” zone radius is the other side of the triangle, side a.
Our formula is now: (green radius)2 + (hand width / 4)2 = (thumb length)2
Now we can solve for the green radius: green radius = √ (thumb length)2 – (hand width / 4)2
To calculate the yellow reach zone, we simply added 1 inch to the green natural zone. Anything beyond that was considered in the red, the unreachable zone.
We followed a very similar calculation to determine the hand size necessary to reach the entire screen of various smartphones. Using the dimensions of each phone, we were able to calculate the distance between the fixed thumb location and the upper left corner of the phone. We then subtracted 1 inch from these lengths to get the radius of the natural zone.
Going back to our formula, we have: (green radius)2 + (hand width / 4)2 = (thumb length)2
Except we know the green radius, and not the other two variables. After taking five measurements of men’s hands, we determined the average ratios between various parts of the thumb. We calculated that the thumb length = 0.866 * hand width, and hand height = 2.061 * hand width.
We can now simplify our formula to: r2 + (0.25w)2 = (0.866w)2
Solving for the width, we get: w = √ r2 / 0.687456
We also used these ratios to help calculate the hand height and width of the famous athletes, where often times only height or span was listed.
- Average hand size for men and women – http://www.theaveragebody.com/average_height.php
- Robert Wadlow – http://www.guinnessworldrecords.com/world-records/11000/largest-hands-ever
- LeBron James, Michael Jordan, Shaquille O’Neal – http://www.foxsportsradio.com/articles/the-locker-room-486404/the-largest-hands-in-the-nba-12467252 and http://www.insidehoops.com/forum/showthread.php?t=257270
- Russell Wilson, Colin Kaepernick – http://www.rotoworld.com/articles/nfl/47036/311/exploring-qb-hand-size
- iPhone 6, 6 Plus, Samsung Galaxy S5, Galaxy Note 4 – http://www.gsmarena.com/