Bond Duration Calculator
Calculate Macaulay Duration, Modified Duration, and convexity for fixed-income bonds.
Estimate price sensitivity to interest rate changes.
What Is Bond Duration? Duration measures a bond’s sensitivity to interest rate changes. It represents the weighted average time until all cash flows are received, with weights proportional to the present value of each cash flow. A higher duration means the bond’s price is more sensitive to rate changes.
Macaulay Duration Developed by Frederick Macaulay in 1938 in the United States, this measures the weighted average time to receive all cash flows. For a bond paying annual coupons: D_Mac = Sum of [t * PV(CF_t)] / Bond Price. Where t is the time period and PV(CF_t) is the present value of the cash flow at time t.
Modified Duration Modified Duration adjusts Macaulay Duration for the yield: D_Mod = D_Mac / (1 + y/n). Where y is the yield to maturity and n is the number of coupon payments per year. Modified Duration directly estimates the percentage price change: dP/P = -D_Mod * dy. For example, if Modified Duration is 5 and rates rise by 1%, the bond price falls approximately 5%.
Convexity Duration gives a linear approximation of price change, but bond prices actually follow a curved relationship with yields. Convexity measures this curvature. Higher convexity means the bond price rises more than expected when rates fall and falls less than expected when rates rise — this is desirable.
Practical Rules Longer maturity means higher duration. Lower coupon means higher duration. Zero-coupon bonds have Macaulay Duration equal to their maturity. Lower yield means higher duration. Bond portfolio managers use duration to manage interest rate risk.