The Most Mathematically Efficient Way to Wrap Your Gifts

The Most Mathematically Efficient Way to Wrap Your Gifts

Inq's Wrapping Paper


Decorative gift wrap as we know it was invented in 1917 at the Hall Brothers stationary store in Kansas City, Missouri! (before that, people used plain brown or tissue paper). It was such a hit that in ten years, it became their primary source of business, and the brothers renamed the company – to Hallmark. Today, people spend more than $3.2 billion on wrapping paper every year.


In the annals of scientific research, there are some interesting scientific studies on gift giving. In case you’re curious as you do your holiday shopping, researchers have discovered that expensive gifts are not more appreciated that cheaper ones, and sentimental gifts are appreciated more than ones keyed to the recipient’s hobbies. But we’re more interested in the science of gift wrapping – and there’s some neat stuff there, too.


The first thing to know is that people prefer wrapped gifts; if you give someone a present that’s wrapped, they have a more favorable attitude towards whatever’s inside the box. Scientists speculate that by activating happy birthday and holiday memories, wrapping paper elevates the mood of the person getting the gift. 


And incredibly, how well you wrap the gift can influence how much somebody enjoys it, but not the way you might expect! In one study, people enjoyed sloppily wrapped gifts about 8% more than neatly wrapped ones (the scientists used the same gift both times). It’s all because of a psychological concept called “expectation disconfirmation”: the gap between what you’re expecting and what you get. A neatly wrapped gift raises the preconceived expectation of what’s inside, and the sloppily wrapped one lowers it. So once the present is unwrapped, the sloppy one seems cooler.


But that’s not always the case. The one time when neatness counts? If you don’t know the person all that well. Studies show that if you’re just an acquaintances with someone, the way a present is wrapped is interpreted as reflecting how you feel about them: if it’s neatly wrapped, they believe you think the relationship is important, if it’s a sloppy mess, then not so much. With close friends, your bond is already strong, so how nicely you wrap the gift doesn’t seem to affect people’s attitudes towards the relationship. These two studies were conducted by the same team, and provide the best answer that science could give you about wrapping a gift: if you barely know someone, make sure those edges are sharp, but with good friends, a sloppy wrapping job is better. So don’t worry about the perfect bow for your bestie, it’s what’s inside that counts!


And finally, if you’ve wondered about the most efficient way to wrap presents, British mathematician Sara Santos has calculated some formulas that use simple measurements to calculate the least amount of wrapping paper needed to cover each gift.

  • For a rectangular present, the formula is: ½ (depth + height + width)2,
  • For a square one, 2(width + height)2


In practice, that means

  • First, measure the present along it’s longest diagonal (in inches or cm, unless it’s super large)
  • Add that to 1 ½ times the length
  • Cut out a piece of wrapping paper of that length on each side, then
  • Set the present on that piece of wrapping paper diagonally, and pull up all four corners into the center.

 Not only do you need the least amount of paper, you’ll only use one piece of tape! 


Now that you’re armed with all the best science and math on the wrapping of gifts, we hope both you and the people you give gifts to enjoy this optical illusion paper – and the holiday season!


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