In economics arc elasticity is defined as the percentage change in one variable when there is a percentage change in another variable. But there is a change in the way the percentage change is calculated. If the value of any of the quantities changes from X1 to X2, the percentage change is not taken as (X2-X1)/X1 but instead the base used is the average of X1 and X2. This gives the percentage change as (X2 - X1)/ ((X2 + X1)/2).
For a variable X changing with respect to a variable Y and a movement from point (X1, Y1) to (X2, Y2) the arc elasticity is [(X2 - X1)/(X2 + X1)/2)]/[(Y2 - Y1)/(Y2 + Y1)/2)]. The use of the average as a base while calculating the percentage change instead of one of the points, gives an equal arc elasticity whether the change is from (X1, Y1) to (X2, Y2) or it is from (X2, Y2) to (X1, Y1).
There are two concepts of elasticity related to each other, they are point elasticity and arc elasticity. point elasticity is when the changes in price and the resultant changes in quantity demanded are infinitesimally small. there will not be any significant difference in the coefficient of elasticity. but in case of arc elasticity, when price change is quite large or when when we have to measure elasticity over the arc of a demand curve rather at a specific point. through arc elasticity we can measure accurate change in demand at give price.