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It is quantified in two ways, Macualay duration and modified duration.
Macaulay duration is the the weighted average maturity of a bond where the weights are the relative discounted cash flows in each period.
Modified duration is calculated as follows:
where r is the yield to maturity of the bond.
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. As interest rates change, the price is not likely to change linearly, but instead it would change over some curved function of interest rates. Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question. Then the convexity would be the second derivative of the price function with respect to the interest rate.
The sensitivity of a portfolio of bonds such as a bond mutual fund to changes in interest rates can also be important. The average duration of the bonds in the portfolio is often reported. The average duration can be used similarly to the duration of a single bond to infer how the price of the portfolio would change in response to changes in interest rates.
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