Bond Macaulay Duration Calculator
Compute a bond’s Macaulay duration — the cash-flow-weighted average time to receive its payments — and its modified duration.
How it works
Macaulay D = Σ [t · PV(CFₜ)] / Price · Modified D = Macaulay D / (1 + y) · (t in periods, then ÷ freq for years)
Macaulay duration is the weighted-average time until a bond’s cash flows are received, with each time weighted by the present value of that cash flow as a share of the price. It doubles as a risk measure: modified duration — Macaulay divided by (1 + periodic yield) — estimates the percentage price change for a one-point move in yield. Longer maturities and lower coupons both push duration up, meaning more price sensitivity to interest rates.
Worked example
For a $1,000 bond, 5% coupon semiannual, 10 years, yielding 6%: discounting each of the 20 cash flows and weighting by time gives a Macaulay duration of about 7.99 years. Dividing by (1 + 0.03) gives a modified duration of about 7.76 years, so a 1% rise in yield implies roughly a 7.76% price drop.
Sources: Bond duration — Wikipedia
Frequently asked questions
What does duration actually measure?
Macaulay duration is the average time, in years, that you wait to receive a bond’s cash flows, weighted by their present values. Modified duration turns that into a sensitivity: the approximate percent price change for a one-percentage-point change in yield.
Why do lower coupons mean higher duration?
With smaller coupons, more of the bond’s value sits in the distant face-value repayment, pushing the weighted-average timing later and raising duration — and therefore interest-rate risk.
Is duration the same as maturity?
Only for a zero-coupon bond, whose single payment sits at maturity. Any coupon-paying bond has a duration shorter than its maturity because it returns cash along the way.
Related calculators
Educational financial-math tool, not investment or financial advice.