Modified Duration Calculator
Modified duration tells you how sensitive a bond's price is to changes in yield. It is computed from the bond's Macaulay duration, the annual yield to maturity, and the number of coupon periods per year. This calculator returns the modified duration and an estimated percentage price change for a yield move you specify. Remember the estimate is a linear approximation; for large yield swings, convexity adjusts the figure.
Modified duration formula
Yield per period = annual YTM / periods per year
Modified duration = Macaulay duration / (1 + yield per period)
Estimated price change (%) = -modified duration * change in yield * 100
Change in yield is entered in percentage points and converted to a decimal (1 point = 0.01) before applying the formula. The negative sign reflects that prices fall when yields rise.
Worked example
Macaulay duration 7 years, 6 percent YTM, semiannual (2 periods), 1 point yield rise:
- Yield per period = 0.06 / 2 = 0.03.
- Modified duration = 7 / 1.03 = 6.80 years.
- Price change = -6.80 * 0.01 * 100 = -6.80 percent.
Modified duration: frequently asked questions
What is modified duration?
Modified duration measures how much a bond's price changes when its yield changes. It is derived from Macaulay duration by dividing by one plus the periodic yield: modified duration = Macaulay duration / (1 + yield per period). A modified duration of 7 means the price falls about 7 percent for a 1 percentage point rise in yield.
How is the price change estimated?
The first-order estimate is: percentage price change is approximately negative modified duration times the change in yield. For a modified duration of 7 and a yield increase of 0.5 percentage points, the estimated price change is about -7 times 0.005, or -3.5 percent. This is a linear approximation; convexity refines it for larger moves.
What is the periods-per-year input for?
Bonds usually pay coupons more than once a year. The yield per period equals the annual yield to maturity divided by the number of coupon periods per year. For a semiannual bond, divide the annual yield by 2. This is the figure used in the (1 + yield per period) denominator.
Why is modified duration always a bit less than Macaulay duration?
Because modified duration divides Macaulay duration by (1 + yield per period), a number greater than one whenever the yield is positive. So modified duration is slightly smaller. The two are equal only at a zero yield, where the divisor is exactly one.
Official sources
- U.S. Securities and Exchange Commission, Investor.gov: Duration.
- U.S. Securities and Exchange Commission, Investor.gov: Bonds.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.