Modified Duration Calculator
Modified duration is a key measure of a bond's interest rate risk. It tells you how much the bond's price will change (as a percentage) for each 1 percentage point change in yield. A higher modified duration means greater price sensitivity. Portfolio managers use duration to manage interest rate exposure and to immunize liabilities. This calculator computes Macaulay duration (weighted average time to cash flows) and then converts it to modified duration using the yield to maturity. Enter the bond's face value, coupon rate, years to maturity, and yield to maturity. Coupons are assumed to be paid annually.
Duration formulas
Macaulay duration = sum(t * PV(CF(t))) / Bond price
where PV(CF(t)) = CF(t) / (1 + y)^t
Modified duration = Macaulay duration / (1 + y)
Price change % = -Modified duration * yield change
Each coupon payment and the final face value repayment are discounted to present value at the YTM. The weight of each cash flow is its present value divided by the total bond price. The weighted average time is the Macaulay duration.
Duration and portfolio management
- A bond with modified duration 8 will fall approximately 8% in price if yields rise by 1 percentage point.
- Short-duration bonds are less sensitive to rate changes; long-duration bonds offer more price appreciation when rates fall.
- Duration matching: if a portfolio's duration equals the investment horizon, interest rate risk is largely neutralized.
- Convexity adjusts for the curvature in the price-yield relationship and improves accuracy for large yield changes.
- Zero-coupon bonds have Macaulay duration exactly equal to their years to maturity, making them the purest duration instruments.
Frequently asked questions
What is modified duration?
Modified duration measures the percentage change in a bond's price for a 1% (100 basis points) change in yield. A modified duration of 7 means the bond price will fall approximately 7% if yields rise by 1 percentage point.
What is Macaulay duration?
Macaulay duration is the weighted average time (in years) until a bond's cash flows are received, where weights are the present values of each cash flow. It is the foundation for calculating modified duration.
How are Macaulay and modified duration related?
Modified duration = Macaulay duration / (1 + y/n), where y is the annual yield to maturity and n is the number of coupon periods per year. For annual coupon bonds (n=1), modified duration = Macaulay duration / (1 + y).
Which bonds have higher duration?
Bonds with longer maturities, lower coupon rates, and lower yields have higher duration and are more price-sensitive to interest rate changes. Zero-coupon bonds have Macaulay duration equal to their time to maturity.
How do I use duration to estimate price change?
Approximate price change % = -modified duration * change in yield (as a decimal). For example, with modified duration 5 and a yield increase of 0.5%, the bond price falls approximately 5 * 0.005 = 2.5%. This is a linear approximation; convexity improves accuracy for larger yield changes.
Official sources
- U.S. Treasury: TreasuryDirect - Bond Data.
- Federal Reserve: Selected Interest Rates (H.15).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.