Measure a bond's interest-rate risk. Enter the coupon, maturity and yield (or price) to get Macaulay duration, modified duration, DV01 and convexity, then see how much the price would move if yields rise or fall.
Last updated:
I know the bond's
Bond
$
%
%
$
years
Rate change scenario
bp
100 bp = 1 percentage point. Negative for a fall.
$
Enter your values to see the result.
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How to use the Bond Duration Calculator
Choose whether you know the yield or the price of the bond.
Enter face value, coupon rate, years to maturity and coupon frequency, plus the yield or price.
Enter a yield change in basis points and optionally your position size.
Press Calculate duration to see Macaulay and modified duration, DV01, convexity and the price change.
Review the scenario and cash flow tables to see where the duration comes from.
Duration formulas
Macaulay duration = Σ t × PV(CFt) ÷ Price, with t in years
Modified duration = Macaulay ÷ (1 + y ÷ m), where y is the annual yield and m the coupons per year
DV01 = Modified duration × Price × 0.0001
Convexity = Σ k(k + 1) × PV(CFk) ÷ [Price × (1 + y ÷ m)2 × m2], with k the period number
Example: a 1,000 bond with a 5% semi-annual coupon, 10 years to maturity and a 6% yield is priced at 925.61. Its Macaulay duration is 7.89 years, modified duration 7.67 and DV01 about 0.71.
If yields rise 1 point to 7%, duration alone predicts a fall of 70.95; adding convexity gives 67.63, close to the exact fall of 67.74 (new price 857.88).
Modified duration of bonds at a 5% yield (semi-annual)
Maturity
0% coupon
3% coupon
5% coupon
7% coupon
2 years
1.95
1.91
1.88
1.86
5 years
4.88
4.55
4.38
4.23
10 years
9.76
8.36
7.79
7.38
20 years
19.51
13.94
12.55
11.72
30 years
29.27
17.27
15.45
14.49
Duration grows with maturity but more slowly for high-coupon bonds, because more of their value arrives early as coupons.
Using duration in practice
Match duration to your time horizon. If you need the money in about 5 years, a portfolio with a 5-year duration is roughly protected against rate changes because price losses and higher reinvestment income offset.
Add up DV01s. Position DV01s are additive, so you can sum them to see the total gain or loss per basis point across a portfolio.
Duration changes over time. As a bond ages and as yields move, its duration changes. Recalculate it rather than relying on an old figure.
Frequently asked questions
What is Macaulay duration?
Macaulay duration is the weighted average time until a bond's cash flows are received, where each payment's weight is its present value as a share of the bond price. A 10-year bond with a 5% semi-annual coupon priced at a 6% yield has a Macaulay duration of about 7.89 years.
What is modified duration and how is it different?
Modified duration = Macaulay duration ÷ (1 + periodic yield). It measures price sensitivity: the approximate percentage change in price for a 1 percentage point change in yield. A modified duration of 7.67 means the price falls roughly 7.67% if yields rise by 1%.
What is DV01?
DV01 (dollar value of an 01, also called PVBP) is the change in a bond's price for a 1 basis point (0.01%) change in yield. It equals modified duration × price × 0.0001. Traders use it to size and hedge positions.
Why do I need convexity?
Duration assumes price changes in a straight line, but the true price-yield curve bends. For large yield moves the duration estimate overstates losses and understates gains. Adding ½ × convexity × (Δy)² × price corrects most of that error.
What is the duration of a zero-coupon bond?
A zero-coupon bond has only one cash flow, at maturity, so its Macaulay duration equals its time to maturity. Its modified duration is that time divided by (1 + periodic yield).
What makes a bond's duration longer?
Longer maturity, a lower coupon and a lower yield all increase duration. Low-coupon bonds have more of their value in the final repayment, which is far away, so they are more sensitive to interest rates than high-coupon bonds of the same maturity.
Does this calculator handle callable bonds?
No. It computes duration for an option-free bond held to maturity. Callable and mortgage-backed bonds need effective duration, which reprices the bond with an option model when yields shift.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.