Macaulay and modified duration — how much a bond's price moves when yields move.
Estimate only — not investment advice. Assumes fixed coupons, no embedded options and parallel yield shifts.
modified duration (years) — price sensitivity
How to use this tool
Type the par value and the annual coupon rate.
Type the yield to maturity and the years remaining.
Semi-annual is standard for most bonds; the calculator annualises duration accordingly.
Macaulay is the average time to get your money back; modified is the one that translates a yield move into a price move.
Formula & worked example
Worked example (zero-coupon check): a 5-year zero-coupon bond has Macaulay duration exactly 5.00 years; at 5% yield, modified duration = 5 ÷ 1.05 = 4.76 years, so a 1-point yield rise cuts its price by about 4.76%. A 10-year 5% coupon bond at 6% yield (semi-annual) has Macaulay duration about 7.9 years and modified duration about 7.7 years.
Limitations — read this before you rely on it
Estimate only. Duration is a linear approximation that is accurate only for small, parallel yield shifts; large moves need convexity too. It assumes fixed coupons, no options, no credit-spread change and a flat yield curve.
Frequently asked questions
The weighted-average time until a bond's cash flows arrive, weighted by present value. For a zero-coupon bond it equals the maturity; for coupon bonds it is shorter.
Macaulay duration adjusted for the yield level: modified = Macaulay ÷ (1 + yield ÷ payments per year). It directly estimates price sensitivity.
Roughly, a 1-percentage-point rise in yield cuts the bond's price by about 7%, and a 1-point fall raises it by about 7%.
Because coupons return money before maturity. Higher coupons and higher yields both shorten duration.
Only approximately — duration is a straight-line estimate. For large moves, add the convexity correction.