Bond Duration & Convexity Calculator

Bond inputs

If you don't know YTM, use the Bond Yield Calculator first, then bring the YTM here.

Face value (par)

Coupon rate (annual %)

Yield to maturity (YTM, %)

If the bond trades at par, YTM equals coupon rate. If at a discount, YTM > coupon. If at premium, YTM < coupon.

Years to maturity

Payment frequency

Number of $1,000-face bonds (portfolio sizing)

Used to scale the dollar-duration and the rate-shock scenarios to your actual position size.

Duration & convexity result

YOUR BOND'S INTEREST-RATE SENSITIVITY

Compute to see your duration figures.

Macaulay Duration

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Weighted-average years to cash-flow receipt.

Modified Duration

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% price change per 1% yield change.

Dollar Duration

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$ price change per 1% yield change.

Convexity

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Second-order curvature term.

Rate-shock scenarios — what happens to price if the yield curve moves

Price impact is computed using both duration alone (first-order) and duration plus convexity (second-order). For small moves (<50bps) the difference is small. For large moves the convexity correction matters — and is always positive for vanilla bonds (the price-yield curve is convex).

PRACTICAL READING

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Cash-flow weighted-time build — the Macaulay calculation, line by line

Macaulay duration is literally the weighted-average time-to-cash-flow, where the weights are the PV of each cash flow divided by the bond's total PV (price). First and last few periods shown.

Show the math — duration as weighted-average cash-flow time, convexity as the second derivative ›

Macaulay Duration — the weighted-average time you wait to receive each cash flow, weighted by the present value of that cash flow.

D_Macaulay = Sum [t=1..n] (t × PV(CF_t)) / Price

It is expressed in years (after dividing the period index by the payment frequency). A zero-coupon bond has Macaulay duration exactly equal to its maturity. A coupon bond has duration less than maturity because the coupons return some cash flow earlier.

Modified Duration — the percentage price change per 1 percentage point change in yield.

D_Modified = D_Macaulay / (1 + y/m)

If modified duration is 7.5, a 1% rise in YTM produces approximately a 7.5% drop in price. The negative sign is implicit (yields and prices move opposite).

Dollar Duration — modified duration multiplied by current price, expressed in dollars.

D_Dollar = D_Modified × Price × 0.01

That is the dollar change in price for a 1% yield change — useful for portfolio aggregation and for hedging via Treasury futures.

Convexity — the second derivative of price with respect to yield, normalized by price.

Convexity = Sum [t=1..n] (t × (t+1) × PV(CF_t)) / (Price × (1 + y/m)^2 × m^2)

The full duration + convexity price-change approximation:

%ΔP ≈ −D_Modified × Δy + ½ × Convexity × (Δy)^2

Convexity is always positive for vanilla (non-callable) bonds, which means the duration-only estimate understates the price gain when rates fall and overstates the price loss when rates rise. The bigger the rate move, the bigger the convexity correction.

Convexity-favorability of long-duration bonds. A 30-year zero has enormous convexity. That's why insurers and pension funds buy them: they get the convexity bonus that hedges against extreme rate moves.

What the tool does NOT model. Callable bond convexity goes negative when rates fall below the call price (the option is exercised, capping the upside). Mortgage-backed convexity is famously negative (prepayments accelerate when rates fall). For those instruments, OAS modeling is required, which is beyond a deterministic-cash-flow tool.

FREE DOWNLOADS · BLOOMBERG-PARITY WORKBOOK + METHODOLOGY

Take the full workbook and methodology PDF

Bond Duration & Convexity Workbook (.xlsx) — Single-bond risk profile, 10-bond portfolio with weighted metrics, ±300bp sensitivity table with vs without convexity, reference tab & disclosures. Free.
Download the workbook
Methodology PDF (18 pp) — Full derivations for Macaulay, modified duration, DV01, and convexity. Positive vs negative convexity, effective duration, key-rate duration. Excel formula reference. Sources.
Open the methodology PDF

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Related tools & guides

Compute YTM, current yield, after-tax yield first → Bond Yield Calculator (YTM / YTC / After-Tax)
Build a duration-laddered portfolio to smooth rate risk → Bond Ladder Builder
Compare a taxable yield to a municipal alternative → After-Tax Municipal Bond Yield
Debt management at the corporate level → CFO Guide — capital allocation, debt issuance, refinancing decisions.
First Principles Guide + the Family Office Reference — fixed-income allocation and duration matching to liabilities.

Disclosure. This tool produces an educational planning estimate for vanilla, non-callable bonds. Callable bonds, MBS, and other instruments with embedded options have option-adjusted duration and convexity that this tool does not compute. Duration approximation is most accurate for small yield changes (<100bps); for larger moves, even the convexity-corrected formula understates true price impact. Real-world bond positions also have credit duration, spread duration, and tax-loss-harvest considerations not modeled here. This is not investment advice. baratelliinstitute.com

If rates move 100 basis points, what happens to this bond's price? Duration tells you. Convexity refines it.

Bond inputs

Duration & convexity result

Rate-shock scenarios — what happens to price if the yield curve moves

Cash-flow weighted-time build — the Macaulay calculation, line by line

Same subject. Four levels of depth.

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