Soccer and Physics

Ben, an adult amateur player, asks:

Why does the air pressure affect the distance the ball travels?


Interesting question – ready-made for an answer chock full of equations and lots of physics, but we’ll rein in our enthusiasm and try not to get technical.  The answer depends on what the ball is traveling on.

When the ball is in continuous contact with the surface of the pitch (i.e., it is rolling), the pressure of the ball determines the rigidity of the surface of the ball (higher pressure = more rigidity) which in turn has a measurable though not easily visible effect on the total surface area of the ball that is in actual contact with the ground’s surface.  At higher pressures, the area of contact is smaller (because the ball is “rounder”) and thus there is less friction on the passage of the ball across the pitch surface.  There is a smaller, secondary effect at higher pressure caused by a somewhat greater “lift” that makes the ball ride a bit higher on the pitch surface.  Remember, a ball is, in effect, a type of balloon – the more air there is in it, the lighter it is and, as with “roundness,” this reduces slightly the contact surface area.  In short, a higher pressure produces a speedier ball, all other things equal.

However, the other medium on which a ball travels is the air.  Here, again, air pressure acts similarly (see above).  A rounder ball (a function of air pressure)  encounters less “drag” while in the air and has greater buoyancy.  There is a third factor regarding a ball traveling in the air that is not found when a ball is rolling on the ground and that is the fact that, inevitably, a ball in the air comes down and makes contact with the ground.  Holding all other factors equal, a higher ball pressure makes for a higher bounce (a factor that you can often actually hear by listening to the sound of the contact – a ping rather than a thud in extreme cases!).  Now, however, something else comes into play (no pun intended) and that is the angle at which the ball is traveling just prior to contact with the ground.  It isn’t speed as such (as is the case with rolling) but it does directly affect distance – which, in a soccer game, may be just as important as the speed of the ball.  With higher air pressure comes greater bounce when the contact occurs – the more acute the angle, the greater the distance for any given air pressure as a result of the bounce effect.

So, the higher the pressure (within the range permitted by Law 2, of course), the greater is the rolling speed and the greater the rolling speed, the longer is the distance the ball will roll (assuming someone from the other team doesn’t stop it!).  This generalization also assumes a relatively constant consistency in the surface (one of the reasons why, again all other things equal, soccer balls travel faster on artificial surfaces relative to grass, and faster on short grass than taller grass).  Further, for a ball launched into the air, the higher the pressure is, the greater the distance traveled both before and after “the bounce” for contact at any angle of less than 90 degrees behind the ball (disregard all forms of spin … it gets too complicated).

There — not a single formal physics lecture and no equations!  Instinctively, though, a home team which has been coached to engage in fast play will likely provide the Referee with game balls at the upper end of the allowable pressure range.  A different team, which may not like or be used to fast play, is likely to provide game balls at the lower end of the pressure range.  It is not the Referee’s job to deliberately favor one team or another by changing an allowable ball pressure up or down based on personal preferences.  If it is in the allowable range, leave it alone.  If it is not, give it to the home team (it’s their ball anyway) for correction but be sure to check a corrected ball again and, again, leave it alone if it is in the allowable range.…


What happens if the ball bursts after being kicked and made contact with during a penalty kick?

Answer (March 6, 2014):
Your answer is contained in Law 2 (THE BALL) of the current Laws of the Game:

Replacement of a defective ball
If the ball bursts or becomes defective during the course of a match:
• the match is stopped
• the match is restarted by dropping the replacement ball at the place where the original ball became defective, unless play was stopped inside the goal area, in which case the referee drops the replacement ball on the goal area line parallel to the goal line at the point nearest to where the original ball was located when play was stopped

If the ball bursts or becomes defective during a penalty kick or during kicks from the penalty mark as it moves forward and before it touches any player or the crossbar or goalposts:
• the penalty kick is retaken…


Our Breakfast Club (which meets to watch soccer games) is in an uproar about the famed Five Pound soccer ball of yore. Some say that a Five Pound weight is nonsense, some say it’s a fact due to the leather uptake in water.

A one pound ball cannot absorb four pints of water to equal Five Pounds in weight. BUT, say the myth believers, the ball was once much heavier than the current one pound limit.

So, when did the current weight limit get established and what was allowed before that?

USSF answer February 5, 2010):
Since 1889 the weight of the ball has always been specified as its measure “at the start of play.” Without waterproofing, leather balls became heavy when wet and sometimes dangerous to head because of protruding lacings. Absorption of moisture is no longer a real problem. The original limits of weight, 12 to 15 ounces (“at the start of play”), were raised in 1937 to 14 to 16 oz and have remained so.…


I have sat through the entry level referee clinics several times now and it has seldom been taught by the same guy twice. I do so to give the new referees a chance to meet their assignor and to keep myself in the loop on how they are being taught this year.

One year the instructor said that all balls should be checked by a gauge before the game. This he said was due to differences in construction, ambient temperature, altitude, etc…. The next sighted a ‘rule of thumb’ where you simply push in with two thumbs to get a feel for whether the ball is tight enough. I happen to side with the first of the two, especially knowing the I have some referees that could barely push a ball in at 6 lbs. and others that work in a packing house by day and could easily push in a ball at 18 lbs.

Here in lies my problem. I have a gauge and a back up (as well as one that is on an cordless electric pump that I keep in my bag). All 3 read the balls differently to one degree or another. How do I determine which is right and which one(s) I should throw away?

USSF answer (November 24, 2009):
Different instructors use different methods to make their points. As long as the referee learns that he or she must apply the requirements of Law 2, the Federation and the Law are satisfied.

As to how to judge the suitability of the ball, that is left to the discretion of the referee, based on what is suitable for this particular game.…


Law 2 says that a properly inflated ball is between 8.5 and 15.6 psi at sea level. Lately I have been presented soccer balls which are labeled “inflate to 6-8 psi”. I have insisted that the ball be inflated to at least 8.5 psi. Am I right to assume that the Laws of The Game trump the manufacturer’s label?

USSF answer (September 8, 2009):
The specifications for the ball listed in Law 2 are intended primarily for play at the senior adult and international level. We do not know what sort of balls have been presented to you, but if they “feel” all right for play, we suggest you allow them to be used. Remember that the referee is the sole judge as to whether the ball meets the requirements of Law 2.…


My question has to do with the use of an undersized ball for the taking of a penalty kick. In a BU-13 match (which matches under our league rules require the use of a Size 5 ball), a PK was awarded in the final two minutes of play. The center referee did not inspect the ball and grabbed a Size 4 ball for the PK.  (The use of the other team’s Size 4 ball for the PK marked the second time that undersized ball was in play). As the ball was set, the coaches for the defending team immediately complained about the ball size prior to the PK being taken. The sideline AR noticed this and raised his flag. The center referee ignored the protest and let the kick occur. The kick was partially blocked by the keeper but rolled in the goal off the keepers hands. After the PK conversion and before play resumed, the sideline AR had the center ref inspect the ball, and they confirmed the use of the Size 4 ball for the successful PK. But the center referee refused to have the PK redone at the request of the defending team’s coach, and instead simply removed the ball again from play. The game ended in a 1-0 result. After the match the center referee told the defending team’s coaches that he did not inspect the ball and that he was responsible to do so. But when requested by the defending team’s coaches to note in writing on the match report that an improper Size 4 ball was used for the converted PK, the center referee refused to, noting only in writing that “a Size 4 Ball was used during the match” (at the suggestion of the other sideline AR than the one who had seen the error and raised his flag.) Were the center referee’s actions proper?

USSF answer (October 15, 2008):
Law 5 tells us that the referee “ensures that any ball used meets the requirements of Law 2.” By implication, that means that the balls used in any game must meet the requirements set down by the competition authority. In the case of your scenario, the referee did not follow the Law: He did not properly inspect the ball and thus did not follow the specific requirement of Law 5 that the ball had to meet the standards.

Therefore, the use of an illegal ball (in accordance with the rules of competition) which resulted in a goal (regardless of whether this was during play, during a penalty kick, or during kicks from the penalty mark) requires that the goal be canceled if the problem is discovered prior to the restart. This must be included in the match report if not discovered until after the restart.…


I am a coach as well as a referee (Grade 8). I was coaching a game where the ball did not seem like it was properly inflated. I asked the center referee about it and he responded that it was OK. At the half, I took an electronic pressure gauge to check the PSI and it registered 4.25 PSI, half the required minimum pressure according to Law 2. We notified the referee about this. Although we were the visiting team, we took one of our best balls, check the pressure which read 8.5 PSI – the minimum amount according to Law 2. We told the referee this as well but we felt he took it personally and it made the second half difficult for us. Did we do the right thing or should we have allowed the game to continue with an under inflated ball?

USSF answer (September 15, 2008):
A referee? Took something personally? One of the first things a referee is supposed to develop is his or her composure, taking nothing personally and certainly not making the game more difficult for one team than the other.

As to the pressure, only the referee can judge that. if he or she decided the ball was properly inflated, then it was properly inflated, no matter whether that was good for the game or not. You will encounter all kinds of people functioning as referees. Some are intelligent and some are not. Some care and some do not. Some are there only for the pay, but some (most, we hope) are there for the good of the game.

You will find an earlier answer (September 10) on the site that deals with the reasons for using various air pressures for the game ball(s).…


What is the right air pressure for U12 boys recreational soccer. If there is a right range why would one choose the lower or higher value?

USSF answer (September 10, 2008):
A good question, as the specifications for the balls other than for adult soccer are not included in the Laws of the Game.

Soccer balls for match use come in three different sizes, 3, 4 and 5. Size 3 balls are the smallest balls and are generally used for players under the age of 8; they are generally 23-24 inches in circumference and weigh between 11-12 ounces. Size 4 balls are generally used for players between the ages of 8 and 12; they weigh between 12-13 ounces and have a circumference of 25- 26 inches.  The details on the ball for adult soccer (Size 5) are in Law 2 of the Laws of the Game. The composition and air pressure figures given in Law 2 apply to all the sizes. Only the weights and circumferences would differ for sizes 3 and 4.

The size ball used for U12 boys recreational soccer is up to the competition authority, the people who make the rules for the particular competition — league, cup or tournament. It would likely be a size 4.

The size 5 ball is spherical, made of leather or other suitable material, of a circumference of not more than 70 cm (28 ins) and not less than 68 cm (27 ins), not more than 450 g (16 oz) in weight and not less than 410 g (14 oz) at the start of the match, and of a pressure equal to 0.6 – 1.1 atmosphere (600 – 1100 g/cm2) at sea level (8.5 lbs/sq in 15.6 lbs/sq in).

Pressure figures are relative to the needs of the game. The air pressure to be chosen depends on weather and field conditions, the skill of the players, and, most practically and importantly, ensuring that the ball pressure is within the manufacturer’s specifications (which are often printed on the ball around the inflation point). A higher pressure usually makes a ball tighter and “faster,” in that it bounces higher and farther and requires much greater skill to control it. A lower pressure will soften the ball and slow it down.…


At a youth soccer game, the coach of one team questioned the ref if the game ball was the correct size and weight since he seemed to think it was not. The ball was like playing with a rubber kick ball with a lot of bounce. The ref answered the coach that both sides have the same advantage and disadvantage with this ball and he was not going to change it, even though there were plenty of balls on the sidelines to choose from.
Should a ball be marked somehow showing that it is the proper size and weight for a game? And if so, then it would have been easier for the ref to point this marking out as proof that the ball is correct.

USSF answer (April 16, 2008):
Although the referee has the final decision, the players deserve to play with the best ball available. There are standards for all balls, specifying circumference, weight, and air pressure. A proper soccer ball should be marked with its size (based on the circumference). The referee should guarantee that the weight and air pressure are sufficient for a good contest.…