Macaulay Duration Calculator
Macaulay duration is the present-value-weighted average time until a bond's cash flows are received. It is a core measure of a bond's interest-rate sensitivity and the basis for modified duration. This calculator discounts each coupon and the final principal at the periodic yield, weights each by its timing, and divides by the bond price to give Macaulay duration in years. It also returns the bond price and modified duration, which estimates the price change for a 1 percentage point yield move. Enter face value, coupon rate, yield to maturity, years to maturity, and payments per year.
Macaulay duration formula
y = YTM / freq, n = years * freq, C = face * coupon / freq
PV_t = CF_t / (1 + y)^t, price = sum of PV_t
Macaulay (periods) = sum(t * PV_t) / price
Macaulay (years) = Macaulay (periods) / freq
Modified = Macaulay (years) / (1 + y)
The final cash flow CF_n includes both the last coupon and the face value. The periodic measure is divided by the payment frequency to express duration in years.
Duration context
- Longer maturity and lower coupons both increase duration.
- A zero-coupon bond's Macaulay duration equals its time to maturity.
- Modified duration approximates price sensitivity to small yield changes.
- Duration assumes a parallel shift in yields and is a first-order estimate.
- Convexity refines the estimate for larger yield moves.
Macaulay 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 time is weighted by the present value of that cash flow as a share of the bond's price. It is named after Frederick Macaulay, who introduced it in 1938.
How is Macaulay duration calculated?
Each coupon and the final principal are discounted to present value at the periodic yield. Each present value is multiplied by the period in which it is received, those products are summed, and the total is divided by the bond's price. Dividing by the payment frequency converts periods to years.
What is modified duration?
Modified duration equals Macaulay duration divided by (1 plus the periodic yield). It estimates the percentage change in a bond's price for a 1 percentage point change in yield. A modified duration of 5 implies a price fall of about 5 percent if yields rise by 1 percentage point.
Why does duration matter?
Duration measures interest-rate sensitivity. Longer-duration bonds change more in price when yields move. Investors use duration to gauge risk, match assets to liabilities, and manage portfolio sensitivity to rate changes.
What inputs does this need?
Enter the face value, the annual coupon rate, the annual yield to maturity, the years to maturity, and the number of coupon payments per year. The calculator returns the bond price, Macaulay duration in years, and modified duration.
Official sources
- U.S. Securities and Exchange Commission: Investor.gov.
- Board of Governors of the Federal Reserve System: federalreserve.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.