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About this tool
Calculate a bond's Macaulay duration, modified duration, and convexity to measure its price sensitivity to interest rate changes.
The Bond Duration & Convexity Calculator discounts every coupon and the final principal at the yield to maturity to produce a bond's price, then derives Macaulay duration as the present-value-weighted average time to cash flow, modified duration as Macaulay divided by (1 + yield per period), and convexity as the second-order term. It is for anyone judging how far a bond's price will move when yields shift — a portfolio manager sizing interest-rate risk, or a student checking a fixed-income exercise. It also prints the discounted cash flow schedule so the numbers can be traced rather than trusted.
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In the Inputs panel enter "Face value", "Annual coupon rate (%)", "Yield to maturity (%)" and "Years to maturity", then set "Payments per year" to Annual, Semiannual or Quarterly.
The Result panel recalculates as you type — there is no submit button — or load the "8-year bond" chip from the Examples row to start from 1000 face, 6% coupon, 7% yield over 8 years.
Read modified duration as the headline with the price in the caption, the "Macaulay duration", "Convexity" and "Approx. 1% yield price change" rows, and the Period / Years / Cash flow / Present value schedule; Copy or Download saves bond-duration-convexity-calculator.txt.
Reports the first and second-order sensitivity in one pass, because duration alone systematically overstates the loss when yields rise.
Prints period, time in years, cash flow and present value for each coupon, so a mismatch with your own model can actually be located.
Discounting uses the periodic yield and periodic coupon, so the duration is correct for the payment frequency rather than assuming annual coupons.
Macaulay duration is the present-value-weighted average number of years until you receive the bond's cash flows, expressed in years. Modified duration divides that by (1 + yield per period) and expresses price sensitivity: a modified duration of 6.2 means roughly a 6.2 percent price fall for a 1 percentage point rise in yield.
Use the second-order approximation: percentage price change = -modified duration x change in yield + 0.5 x convexity x (change in yield)². For a 1 percentage point rise, that is -D x 0.01 plus 0.5 x C x 0.0001, which is exactly the figure this calculator reports. Convexity always adds back a little, which is why duration alone overstates losses and understates gains.
Because more of the bond's value arrives early, so the weighted average time to cash flow falls. A zero-coupon bond has a Macaulay duration equal to its maturity, while a high-coupon bond of the same maturity has a noticeably shorter one — and is therefore less sensitive to rate moves.
No. The calculation assumes a plain vanilla bond held to maturity, with fixed coupons, no default, and a single flat yield used to discount every cash flow. Callable, puttable and floating-rate bonds need effective duration computed from repriced scenarios, and any real investment decision should involve a qualified adviser rather than a screening calculation.
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