Bond Duration Calculator (Macaulay & Modified)

Macaulay duration is the present-value-weighted average time (in years) until a bond's cash flows arrive: each coupon (and the face value at maturity) is discounted back to today at the market yield, weighted by how many years away it is, summed up, and divided by the bond's price — duration = Σ(t · PV(cash flowₜ)) ÷ price.

Modified duration rescales that into an interest-rate-sensitivity measure: modifiedDuration = macaulayDuration ÷ (1 + periodic yield). It approximates how much the bond's price moves for a small change in yield: %ΔPrice ≈ −modifiedDuration × Δyield — the estimate shown for a 1 percentage point yield move uses exactly this approximation, so it gets less accurate for larger yield swings (it ignores convexity, the curvature of that relationship).

A zero-coupon bond has exactly one cash flow, at maturity, so its Macaulay duration always equals its years to maturity exactly — set the coupon rate to 0% to see that identity directly. Bonds with higher coupons return more cash sooner, which pulls duration shorter than an otherwise-identical lower-coupon bond.