Vo2Max Calculator using Race Results
Using the result of a race (>3 km) it is possible to estimate your VO2max

Fitness can be measured by the volume of oxygen you can consume while exercising at your maximum capacity. Vo2max is the maximum amount of oxygen in millilitres, one can use in one minute per kilogram of body weight. Those who are fit have higher Vo2max values and can exercise more intensely than those who are not as well conditioned.

This estimate is very subjective and will have a larger margin of error than the cooper test. There are many factors which are not accounted for such as the terrain but is can give you a good indication.