About the Bond Duration Calculator
This bond duration calculator measures a bond’s sensitivity to interest-rate changes. Enter the face value, coupon rate, yield to maturity, years to maturity and how often coupons are paid, and it returns the bond’s price, Macaulay duration, modified duration, convexity and DV01 (the dollar value of a one-basis-point move), plus a cash-flow table.
It is useful for bond investors comparing funds or individual issues, students working through fixed-income problems, and anyone who wants to know how much a bond or bond fund could fall if rates rise. Enter a yield change in basis points to see the estimated price move from duration and convexity next to the exact repriced change.
The calculation assumes a plain fixed-rate, option-free bond priced on a coupon date, with the yield compounded at the coupon frequency. Callable bonds, floating-rate notes and bonds between coupon dates need adjustments (effective duration, accrued interest) that are outside this model.
With the default inputs, the macaulay duration is 7.895 years. Change any value above to recalculate instantly.
How to use the bond duration calculator
- 1Enter the bond’s face value and annual coupon rate.
- 2Enter its current yield to maturity and years left to maturity.
- 3Choose how often it pays coupons (most US bonds are semi-annual).
- 4Read Macaulay and modified duration; modified duration ≈ % price change per 1% yield move.
- 5Enter a yield change in basis points to test a rate rise or fall.
Formula and method
The price P is the sum of every coupon and the final principal repayment discounted at the yield per period y/f. Macaulay duration is the weighted-average time, in years, until those cash flows arrive, where each weight is the cash flow’s share of the price. Modified duration divides Macaulay duration by (1 + y/f) and gives the approximate percentage price change for a 1-point change in yield.
Convexity captures the curvature of the price–yield relationship. The estimated price change for a yield change Δy is −D_mod × Δy + ½ × C × Δy², which is more accurate than duration alone for large moves. DV01 is modified duration × price × 0.0001, the dollar change for a single basis point. The calculator also reprices the bond at the new yield so you can compare the approximation with the exact answer.
- CFₜ
- Cash flow in period t (coupon, plus face value at maturity)
- y
- Annual yield to maturity
- f
- Coupon payments per year
- t
- Period number, 1 to n
- Δy
- Change in yield (1 bp = 0.0001)
Worked examples
10-year 5% semi-annual bond at a 6% yield
Discounting twenty $25 coupons and the $1,000 principal at 3% per half-year gives a price of $925.61. The weighted-average time to cash flows is 7.895 years; dividing by 1.03 gives modified duration 7.665. A 100 bp rise is estimated to cut the price by 7.31%, almost exactly the repriced −7.32%.
Zero-coupon bond
A zero-coupon bond pays everything at maturity, so its Macaulay duration equals its maturity: 5 years. Modified duration is 5 ÷ 1.04 = 4.81, and the price is $1,000 ÷ 1.04⁵ = $821.93.
3-year annual 8% bond priced at par
When the coupon equals the yield the bond trades at par ($1,000). The coupons pull the average time to cash flow below 3 years, to 2.783; modified duration is 2.577, so a 50 bp rise costs about 1.28% of the price.
Frequently asked questions
What is the difference between Macaulay and modified duration?+
Macaulay duration is the weighted-average time, in years, until you receive a bond’s cash flows. Modified duration converts that into price sensitivity: it equals Macaulay duration divided by (1 + yield per period) and tells you the approximate percentage price change for a 1 percentage-point change in yield.
What does a duration of 7 mean?+
A modified duration of 7 means the bond’s price should fall about 7% if its yield rises by one percentage point, and rise about 7% if the yield falls by one point. The estimate is most accurate for small yield changes.
Why does convexity matter?+
Duration assumes a straight-line relationship between price and yield, but the real curve bends. Positive convexity means prices rise more when yields fall than they drop when yields rise by the same amount. Adding the convexity term makes the estimate much closer for moves of 100 bp or more.
What is DV01?+
DV01, also called PV01 or the dollar value of a basis point, is how much the bond’s price changes for a 0.01% change in yield. It is modified duration × price × 0.0001 and is widely used by traders to size and hedge positions.
How does coupon rate affect duration?+
Higher coupons return more of your money earlier, which shortens duration. Longer maturities lengthen it. A zero-coupon bond has the longest duration for its maturity — exactly equal to its years to maturity.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.