Bond Duration Calculator
Duration is the most important measure of a bond's interest rate risk. Macaulay duration is the weighted average time until a bond's cash flows are received, measured in years. Modified duration converts this into a direct estimate of price sensitivity: approximately how much the bond's price will change for a 1% movement in yield. A bond with modified duration of 8 will lose roughly 8% of its value if interest rates rise by 1 percentage point, or gain roughly 8% if rates fall by 1 percentage point. Portfolio managers, risk officers, and individual investors use duration to assess and manage their exposure to interest rate changes. This calculator computes both Macaulay duration and modified duration from your bond's face value, coupon rate, current yield, years to maturity, and payment frequency.
Duration formulas
Macaulay Duration = sum(t x PV(CF_t)) / Bond Price
where PV(CF_t) = CF_t / (1 + r)^t, t = period/freq
Modified Duration = Macaulay Duration / (1 + r)
where r = periodic yield = Annual Yield / freq
Price Change (approx) = -Modified Duration x yield change
Duration rules of thumb
- Zero-coupon bonds: duration equals time to maturity (all cash flow at maturity).
- Coupon bonds: duration is always less than time to maturity.
- Higher coupon rate: lower duration (more cash flow received early).
- Higher market yield: lower duration (future cash flows discounted more heavily).
- Modified duration of 1 means 1% yield change causes approximately 1% price change.
Bond duration: frequently asked questions
What is Macaulay duration?
Macaulay duration is the weighted average time (in years) until a bond's cash flows are received, where each cash flow is weighted by its present value as a share of the bond's total price. It represents the effective maturity of the bond in economic terms.
What is modified duration and why is it useful?
Modified duration equals Macaulay duration divided by (1 + yield/frequency). It measures the approximate percentage change in bond price for a 1% (100 basis point) change in yield. A modified duration of 7 means the bond price will fall roughly 7% if yields rise 1%.
Which bonds have higher duration?
Longer-maturity bonds have higher duration. Lower-coupon bonds also have higher duration because less of the total value is paid out early as coupons. Zero-coupon bonds have duration equal to their maturity because all cash flow occurs at the end.
How do portfolio managers use duration?
Portfolio managers use duration to match asset and liability cash flows (immunisation) or to position a portfolio to benefit from expected interest rate movements. If you expect rates to fall, increasing portfolio duration amplifies price gains. If you expect rates to rise, shortening duration limits losses.
What is convexity and how does it relate to duration?
Duration is a linear approximation of price sensitivity. Convexity captures the curvature: how duration itself changes as yields change. For large yield moves, combining duration and convexity gives a more accurate price change estimate. Higher convexity is generally beneficial for bondholders.
Official sources
- Federal Reserve Bank of San Francisco: Bond Duration and Interest Rate Risk.
- U.S. Treasury: Interest Rate Data.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.