Bond convexity calculator

Calculate a fixed-rate bond’s price, Macaulay and modified duration, convexity and DV01. Compare duration-only and duration-plus-convexity estimates with an exact repricing after a yield change.

CurrencyFormatting only; no exchange-rate conversion.
Face value (par)Principal paid at maturity.
Annual coupon rate (%)Enter 0 for a zero-coupon bond.
Years to maturityYears × payments per year must be a whole period count.
Coupon payments per yearThe yield is nominal and compounded at this frequency.
Yield to maturity (%)A leading minus sign is accepted for a negative yield.
Yield change (basis points)Positive means yields rise; 100 bp = 1 percentage point.

What bond convexity measures

Modified duration gives a straight-line estimate of how a bond price changes when yield changes. The actual price-yield relationship is curved. Convexity measures that curvature and adds a second-order correction, which normally improves the estimate when the yield move is not tiny.

This calculator is for one fixed-rate bond. It does not solve an unknown YTM from a market price; use the Bond Price Calculator for that separate task.

Duration, convexity and price-change formulas

Price = Σ [CF_t ÷ (1 + y/m)^t]

Here, y is nominal annual YTM, m is payments per year, t is the coupon-period number, and the final cash flow includes face value.

Macaulay duration = Σ [(t/m) × PV(CF_t)] ÷ price
Modified duration = Macaulay duration ÷ (1 + y/m)

Convexity = Σ [t(t + 1) × CF_t ÷ (1 + y/m)^t+2] ÷ (price × m²)

Estimated % price change = −modified duration × Δy + ½ × convexity × (Δy)²

The exact comparison price is calculated by discounting every cash flow again at YTM + Δy. DV01 equals price × modified duration × 0.0001 and estimates the currency move for a one-basis-point yield increase.

Checked example

A US$1,000 bond with a 5% annual coupon, 10 years remaining, semiannual payments and a 4% YTM has a modeled price of US$1,081.7572. Macaulay duration is 8.080936 years, modified duration is 7.922486 years and convexity is 75.472467.

If yield rises 100 basis points to 5%, duration alone estimates a −7.922486% price change. Adding convexity changes the estimate to −7.545124% and an estimated price of US$1,000.1372. Exact cash-flow repricing gives US$1,000, so the convexity approximation is US$0.1372 high.

How to interpret the results

Modified duration is the first-order sensitivity. A value of 7.9 means about a 7.9% price move in the opposite direction for a one-percentage-point yield move, before convexity.
Convexity is the second-order curvature measure. It is reported in years squared under the discrete-compounding convention shown above.
DV01 estimates the price loss for a one-basis-point yield increase. Its magnitude is shown as a positive currency amount.
Duration + convexity is still an approximation. The exact repricing column discounts the same contractual cash flows at the changed yield.

Assumptions and limits

Settlement is on a coupon date. Accrued interest, clean-versus-dirty price, day-count conventions and settlement delays are excluded.
The bond is fixed-rate, option-free and pays as promised. Calls, puts, defaults, taxes, inflation linkage and floating coupons require different models.
The yield shift is parallel and the bond’s cash flows do not change. Credit-spread and benchmark-rate movements are not separated.
Inputs are user-supplied, not live quotes. Results are educational estimates, not investment advice.

Related calculators

Use the Bond Price Calculator to solve price or YTM and view current yield; the Bond Ladder Calculator to allocate money across maturities; the Tax Equivalent Yield Calculator for municipal-versus-taxable yield; and the APY Calculator for nominal and effective annual rates.