Macaulay Duration Calculator
Compute a bond’s Macaulay and modified duration — the time-weighted average of its cash flows and its price sensitivity to yield.
How it works
Macaulay = Σ [t × PV(CFₜ)] ÷ price · Modified = Macaulay ÷ (1 + yield) · PV(CFₜ) = CFₜ ÷ (1 + yield)ᵗ
Macaulay duration is the weighted-average time until a bond’s cash flows are received, with each year weighted by the present value of that year’s payment. It captures how "long" the bond effectively is: a zero-coupon bond’s duration equals its maturity, while coupons pull it shorter. Dividing by (1 + yield) gives modified duration, which estimates the percentage price change for a small change in yield — the everyday measure of interest-rate risk.
Worked example
A 5-year bond, 5% annual coupon, priced at par (5% yield). Discounting each year’s cash flow and time-weighting it gives a Macaulay duration of about 4.55 years. Modified duration = 4.55 ÷ 1.05 ≈ 4.33, so a 1% yield rise implies roughly a 4.33% price drop.
Sources: Macaulay duration (Wikipedia)
Frequently asked questions
What is the difference between Macaulay and modified duration?
Macaulay duration is measured in years (the average time to receive cash flows). Modified duration is a percentage sensitivity: it approximates how much the price changes for a 1% change in yield, and equals Macaulay divided by (1 + yield).
Why does a higher coupon shorten duration?
Larger coupons return more of your money sooner, so the weighted-average timing of cash flows moves earlier. A zero-coupon bond returns everything at maturity, giving it the longest possible duration for its term.
Is duration exact for large yield moves?
No. Duration is a straight-line approximation that works well for small yield changes. For big moves the price-yield curve bends, and convexity is needed to correct the estimate.
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Educational estimate, not investment advice. Options and leveraged positions carry substantial risk.