Macaulay Duration (traditionally just called Duration)
The formula usually used to calculate a bond's basic duration is the Macaulay duration, which was created by Frederick Macaulay in 1938, although it was not commonly used until the 1970s. Macaulay duration is calculated by adding the results of multiplying the present value of each cash flow by the time it is received and dividing by the total price of the security.

Modified Duration
Modified duration is a modified version of the Macaulay model that accounts for changing interest rates. Because they affect yield, fluctuating interest rates will affect duration, so this modified formula shows how much the duration changes for each percentage change in yield. For bonds without any embedded features, bond price and interest rate move in opposite directions, so there is an inverse relationship between modified duration and an approximate 1% change in yield. Because the modified duration formula shows how a bond's duration changes in relation to interest rate movements, the formula is appropriate for investors wishing to measure the volatility of a particular bond.

Effective Duration
The modified duration formula discussed above assumes that the expected cash flows will remain constant, even if prevailing interest rates change; this is also the case for option-free fixed-income securities. On the other hand, cash flows from securities with embedded options or redemption features will change when interest rates change. For calculating the duration of these types of bonds, effective duration is the most appropriate.