As an instructor I regularly get phone calls from parents of children as young as three enquiring about Taekwon-Do classes for their child. My own feeling as a parent, teacher and instructor, has always been that this is far too young. However parents seem reluctant to believe me and I know that no sooner have I hung up the 'phone than they will call another Taekwon-Do school to ask the same question until they find someone who will accept them. I recently witnessed a martial arts demonstration in which a child aged around 3 or 4 took part with a dummy in his mouth! I teach children from the age of 6, or 5 if their parents do it too. Still, I wanted some evidence to back up my gut feeling so I decided to do some research.
Bruce Lee, probably the best known and most highly acclaimed martial artist ever was 13 years old when he began his training as was female martial arts film legend Cynthia Rothrock who holds Black Belts in Tang Soo Do, Taekwon Do, Eagle Claw, Wu Shu, and Northern Shaolin. Jean Claude Van Damme was around 11 or 12, whilst film legend Chuck Norris was older at 18. General Choi Hong-Hi, founder of Taekwon-Do, was around the age of 20 when he had his first encounter with martial arts  and Michelle Yeoh of Crouching Tiger and James Bond Tomorrow Never Dies fame, didn't start martial arts training until 22, however she had been doing ballet since the age of 4.
From this it would seem that attaining a high level of success in martial arts is not dependant on a very early start, all these people being above 11 years old. However some other martial arts greats did begin a little younger. Jet Li of The Enforcer and Romeo Must Die fame, was aged 8 when he began  Jackie Chan was 7 , Grandmaster Rhee Ki Ha was around 7 or 8 when he began judo, (his first introduction to martial arts) and Steven Seagal was around 6 or 7 
The starting ages of these martial arts greats ranges from 6 or 7 to 22, but there is little evidence to be found of success by children starting below the age of 6. The lack of evidence could be because this is indeed too young, but there may be other reasons. It may be that in the 1960s and 70s martial arts training was not so widely available for young children and not as popular with parents as a chosen activity for their child, certainly in western cultures.
What about the Shaolin monks? Research suggests that some Chinese children begin their Kung Fu training between the ages of 4 and 10 years although the senior successful monks my research turned up began when they were around 8 to 11 years old  making the evidence inconclusive.
Next I carried out a survey amongst Taekwon-Do Instructors. Thirty seven instructors took part, ranging from 1st to 8th Dan. These included seven Masters/ Senior Masters, all but one of whom began Taekwon-Do at 13 or over, the one exception being Master Andrew Rhee, son of Grandmaster Rhee who might be considered an exception due to his parentage, he began at the age of 7. Twenty out of twenty two 4th to 6th Dans were 13 years old or over, while two were between 10 and 12. Of eight 1st to 3rd Dans, all but one were 13 or older, whilst one was aged just 6. In summary 35 out of 37 instructors began aged 10 or older, one began aged 6 and one 7. Six had tried another martial art at a younger age though none at younger than 7. Still no evidence for the under 6s.
However, the survey did not asked the current age of instructors, so the same could be true as with the 'famous' martial artists, was there less popularity or availability of classes for young children when they were below 6 than there is now?
To investigate further we need to skip to the next generation, the students of these instructors. Of thirty seven instructors, nine had taught children of 3 or 3½ but none had had a 3 year old starter reach black belt. Some of these children may still be training but only one instructor had managed to get a 3 year old starter to at least green belt. Fifteen instructors had taught 4 or 4½ year olds, three of whom had had a child go on to achieve a black belt (in no cases were children the offspring of the instructors). Are these 4 year olds exceptional? With low numbers in the survey it is difficult to know for sure. More interestingly though, I discovered that of 30 instructors who had taught 5 year olds, nine of them (almost a third) had had children go on to achieve black belt. So perhaps 5 is a good age to start in order to be successful.
However, at this point, a further question needs to be asked. Should we consider gaining a black belt as the measure of success? In the survey I suggested you might consider reaching green belt as a measure of success and asked if instructors had other ways to measure it. Some suggestions were that a child's self esteem is raised, or that they enjoy it for at least three months or other named periods of time. A 3,4 or 5 year old child has really no concept of future success, they just know what they want now. The ambition probably comes from the parent, but what does the parent want for their child? To enjoy an activity for a few months? To improve their coordination and confidence? To become a black belt ? To begin an activity for a lifetime? What does the instructor want? What would the child looking back as an adult have wanted for themselves?
One instructor surveyed, pointed out that it was the teenage years when students were most likely to give up, often after having achieved back belt. Is this as a result of starting too early? Could success be measured by a child continuing past the teen years and into adulthood? I personally like this definition of success. Looking back at the evidence, the famous names in martial arts had all begun above the age of 6, yet the evidence from the instructors' survey clearly shows that 5 is a good age to begin in order to progress to black belt. Could early success lead to peaking too early and not continuing the activity for life? Could it be that a slightly later start, above 6 or 7 would give a child a better chance of continuing into adulthood?
The opinions of instructors as to the optimum starting age in order to avoid drop out were mixed, with over a third saying that they didn't think age was relevant, the other two thirds gave ages between 6 and 11+, with most favouring ages 10 or 11+. None suggested 3,4 or 5. A majority of instructors felt that the involvement of parents or older siblings was an important factor in a younger child's ability to continue and succeed. The length of lessons, structure and activities of the class and qualities of the instructor were also cited as relevant factors.
In determining optimum starting age, physiological aspects must also be considered. For example, a child's head is proportionally large and their arms and legs short compared to an adult, thus for example, making the formation of a correct rising block almost impossible, (see photographs - the child on the left is 3, the one on the right is 6). As the child grows, changes in body proportions affect how techniques are performed. For example, changes in the relative size of the head in childhood affects the balance of the body during movement. These factors can slow down the progress of the younger child and although they catch up eventually, they may become bored in the process and give up. A contemporary starting a year or two later would achieve the same standard much more quickly without time for boredom to set in.
By the age of 3, the average child can jump off a step and stand very briefly on one leg, so they could take part in some aspects of a TKD class. However, emotionally at this age children are often clingy, showing fear of separation from parents, and they may show anger or violent outbursts, which would clearly be a problem. By the age of 4 children can usually play cooperatively with other children. Between 4 and 5, they can skip and jump and by 5 they can show responsibility and guilt and feel pride in accomplishments. This sounds more like the level of development needed for a martial arts class, and although the exact age depends on the individual child, instructors may find such milestones a useful guide when setting a minimum age.
When deciding on the starting age, you need to establish what the aim is, which brings me back to my two favoured measures of success. Firstly, achieving a black belt; none of the instructors surveyed have succeeded in taking a 3 year old starter through to black belt and I can find no martial arts 'greats' who started that young. This leads me to conclude that 3 is too young. I would suspect that if someone is reading this and thinking 'I know someone who started at 3 and got a black belt' that one of two things applies, either the child is the offspring of the instructor (which may put a different slant on things) or the 'black belt' is not from an association with proper standards. Some success was shown with 4 year olds although I believe more evidence is needed. A significant amount of success in reaching black belt was shown with 5 year olds, (similar to that of 6 and 7 year olds).
Regarding my second measure of success, staying into adulthood, it seems that a later start gives a better chance. Evidence gleaned about famous martial artists and current Masters and instructors, indicates that starting at 6 or above gives a better chance of continuing into adulthood than a younger start, but starting at 10 or above gives a better chance still.
Some parents like to think their child is the exception, and believe that they will not only continue as long as the parent would like them to, but also be much better for having started earlier. In fact if they did succeed after starting at 3 or 4, evidence shows that they would not be any better than if they had started at 7 or 8. The evidence also points to the increased likelihood of them giving up.
The survey was limited, and didn't take into account numbers of students that individual instructors had taught or succeeded with, or details of those students who had continued as adults. There is a lot more research that could be done in this area. However, I believe there is enough evidence to answer the original question; What is the best age for a child to start a martial art?
For short term benefits such as improved confidence and co-ordination, anything from 4 up. If you want the child to eventually get a black belt, start them from 5. If you want them to get black belt and continue the activity successfully into adulthood, 6 at the youngest, but wait a little longer to improve the odds i.e. between 7 and 10.