Bond Convexity Calculator
This bond convexity calculator shows a bond's convexity, price and periods from coupon, yield and maturity, and how it refines rate risk beyond duration.
What it does
The Bond Convexity Calculator measures the curvature of a bond's price-yield relationship. It complements duration by capturing how a bond's price sensitivity itself changes as yields move, giving a more accurate picture of price behaviour during large interest-rate swings.
Data sources & parameters
This calculator uses standard financial formulas and runs entirely in your browser. It needs no external rate data — your result is computed only from the values you enter above.
We always strive to use the latest data for every variable so our results and reports are as accurate as possible. Even so, errors are possible — you should not rely on this tool or its report alone, and we accept no liability for any decision made based on it.
The formula
Convexity = ( Σ CF_t × t × (t+1) / (1+y)^(t+2) ) ÷ Price ÷ f², where y is the periodic yield and f the coupon frequency
How it works
The tool discounts every coupon and the final principal at the yield to maturity to find the price, then weights each cash flow by t(t+1) and discounts it two extra periods. Dividing that sum by the price and scaling to annual terms gives convexity.
Where it is used
- Refining an interest-rate risk estimate beyond duration alone
- Comparing how two bonds react to large yield moves
- Understanding why long or zero-coupon bonds swing more in price
Worked example
A $1,000.00 bond with a 5% annual coupon priced to a 5% yield over 5 years trades at … with a convexity of … across … periods, meaning its price gains slightly more when yields fall than it loses when yields rise by the same amount.
What the bond convexity calculator does
Enter the face value, coupon rate, yield to maturity, years to maturity and coupon frequency of a plain fixed-coupon bond, and the calculator returns its price, its convexity and the number of coupon periods. Convexity measures the curvature of the price-yield relationship.
Duration tells you how much the price moves for a small change in yield. Convexity tells you how that sensitivity itself changes as yields keep moving. Together they are the two main measures of interest-rate risk.
Why duration is not enough
Duration treats the price-yield relationship as a straight line, which works well for tiny yield changes. The real relationship is a curve: as yields fall, prices rise at an increasing rate, and as yields rise, prices fall at a decreasing rate. So a duration-only estimate understates the gain when yields drop and overstates the loss when they climb. A convexity term corrects both. For small moves the correction is minor; for large swings, ignoring it can misjudge risk and return noticeably.
How convexity is calculated
The calculator prices the bond by discounting every cash flow at the yield to maturity. Each coupon is the face value times the coupon rate divided by the frequency, and the final period also returns the principal.
For convexity, it weights each cash flow by its period number times the next period number, discounts it two extra periods, sums the results, divides by the price, and divides by the square of the frequency to express the answer in annual terms. Later cash flows get much heavier weights, which is why maturity and coupon structure drive the result. Only the bond's own terms are needed, so identical inputs always give identical convexity.
Reading the results
- Bond price: the present value of all coupons and the principal at your yield. Above face value the bond trades at a premium; below, at a discount.
- Convexity: the curvature measure in annual terms. Larger numbers mean the price-yield relationship bends more sharply.
- Number of periods: years times frequency, confirming how the maturity and schedule were read.
Convexity is most useful when compared: next to another bond's figure, it shows which will react better to a large, uncertain move in rates.
What raises convexity
Longer maturities increase convexity, because cash flows lie further out where the curve bends most. Lower coupons increase it, since more value is concentrated at maturity; zero-coupon bonds have the highest convexity at a given maturity. Lower yields raise it modestly. This is part of why a long, low-coupon bond swings far more in price than a short, high-coupon one.
Using convexity
When two bonds offer similar yields and durations, the more convex one usually has the better payoff across rate scenarios. Portfolio managers add convexity ahead of expected volatility, giving up a little yield for the protection. A hedge built on duration alone leaves an exposure that grows with the size of the rate move; matching convexity too tightens it. Liability-driven investors match both so assets and liabilities move together when rates shift sharply.
Limitations
The calculation uses one flat yield for every cash flow and a fixed coupon schedule. Bonds with embedded options, such as callable or putable bonds, can show negative convexity over some yield ranges. This calculator models an option-free bond. Read convexity together with duration, yield and credit quality, and use it to compare scenarios, not to predict an exact price.
This article is general information only and is not financial advice.
About This Bond Convexity Calculator
Use this bond convexity calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.
Frequently asked questions
What is bond convexity?
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