Bond Duration Calculator – Measure Interest Rate Risk in One Place
The Bond Duration Calculator is built to help investors, analysts and students understand how sensitive a bond’s price is to interest rate changes. Duration is one of the most important fixed-income risk metrics. It provides a time-weighted measure of a bond’s cash flows and serves as a practical estimate of price volatility when yields move.
With this tool, you can calculate Macaulay duration and modified duration for a plain-vanilla coupon bond, estimate price changes for yield shocks using duration and convexity, and compute a weighted average portfolio duration for up to three bonds.
What Is Bond Duration?
Bond duration measures the weighted average time it takes to receive the bond’s cash flows, where the weights are the present values of those cash flows. Duration is expressed in years, but its main use is to approximate price sensitivity to yield changes.
For small yield movements, modified duration tells you roughly how much the bond’s price will change in percentage terms for a 1% (100 basis point) change in yield. A longer-duration bond is more sensitive to interest rate movements than a shorter-duration bond.
Macaulay Duration vs Modified Duration
This calculator reports both Macaulay duration and modified duration:
- Macaulay duration: The present value weighted average time to receive cash flows, measured in years.
- Modified duration: Macaulay duration adjusted for the bond’s yield. It approximates the percentage price change for a 1% change in yield.
Single Bond Duration – How It’s Calculated
In the Single Bond Duration tab, you enter:
- Face value
- Annual coupon rate
- Yield to maturity (YTM)
- Years to maturity
- Coupon payment frequency
The calculator constructs a schedule of coupon payments plus the final principal repayment, discounts each cash flow at the bond’s yield per period, and then computes both price and duration.
Bond Price and Duration Formulas
where CFt is the cash flow in period t, y is the annual yield, and m is the number of payments per year.
Timet is measured in years, so each period t is converted to t ÷ m.
The calculator shows the bond price, Macaulay duration, modified duration and the average time of cash flows in years.
Price Sensitivity – Duration and Convexity
Duration alone works best for small yield changes. For larger rate moves, convexity helps refine the estimate. In the Price Sensitivity tab, you can enter a yield change in percentage points (for example, 1 for a 1% increase in yield). The tool recalculates duration and an approximate convexity measure based on the same cash flows.
The approximate percentage price change is then estimated using:
Here Δy is the change in yield expressed as a decimal (for example, 0.01 for 1%). The calculator reports the current price, modified duration, approximate convexity, estimated percentage price change and the resulting new price.
Portfolio Duration – Weighted Average Risk
Most investors hold portfolios of bonds rather than a single instrument. Portfolio duration is a useful summary of overall interest rate risk. In the Portfolio Duration tab, you can input up to three bond durations and their weights (for example, portfolio allocations in percent).
The calculator computes a weighted average duration, normalized so that weights sum to 100% even if your raw inputs differ slightly. This gives a simple approximation of how sensitive the whole portfolio is to parallel shifts in the yield curve.
Practical Uses of Bond Duration
Duration is central to fixed-income risk management. You can use this calculator to:
- Compare interest rate sensitivity across bonds with different coupons and maturities.
- Estimate how much a bond’s price might move if yields rise or fall.
- Align bond holdings with a specific interest rate view or investment horizon.
- Design a bond ladder or portfolio with a target duration.
- Teach or learn core concepts in bond math and interest rate risk.
Limitations and Assumptions
The calculations assume:
- A plain-vanilla, fixed-rate bond with known coupon payments and a single maturity date.
- Yield is compounded at the chosen payment frequency.
- Parallel shifts in the yield curve when estimating price changes.
Real-world bonds may have embedded options, call features or different day-count conventions, which can affect effective duration and convexity. For such instruments, more advanced models are required.
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Bond Duration Calculator FAQs
Frequently Asked Questions Bond Duration
Get quick answers Macaulay duration, modified duration, price sensitivity and portfolio duration.
A duration of 7 years means that, for a small parallel change in yield, the bond’s price will change by roughly 7% in the opposite direction for a 1 percentage point move in yields. It also indicates that the average time to receive cash flows is 7 years.
Longer-maturity bonds have cash flows further in the future, which are more sensitive to discount rate changes. Unless coupons are very high, this typically results in a higher duration and greater price volatility when yields move.
Yes. Higher coupons bring more cash flows to earlier years, which lowers the weighted average time of cash flows and typically reduces durationative to a low-coupon bond with the same maturity and yield.
This calculator assumes non-callable, fixed-rate bonds with known cash flows. Callable or putable bonds require option-adjusted measures such as effective duration, which are not covered here.
Weights are often based on market value (for example, the proportion of total portfolio value in each bond). You can also use target allocation percentages. The calculator will normalize your weights to sum to 100%.