Bond Duration & Convexity Calculator

Compute a bond’s price, Macaulay duration, modified duration, and convexity from its coupon, yield to maturity, and term.

Inputs

Par value repaid at maturity.

Coupon rate as a percent of face value.

Market yield to maturity (per year).

Time to maturity in years.

Coupon payment frequency.

Result

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How to use this calculator

  • Enter the face value, coupon rate, yield to maturity, and years to maturity.
  • Choose the coupon frequency (annual, semiannual, quarterly).
  • Read the bond price, Macaulay and modified duration, and convexity.
  • Use modified duration and convexity to estimate price moves for yield changes.

About this calculator

Duration and convexity describe how a bond’s price responds to interest-rate changes. This calculator first prices the bond by discounting every coupon and the final principal at the yield to maturity. Macaulay duration is the present-value-weighted average time until you receive the bond’s cash flows, in years. Modified duration adjusts that into a sensitivity: it estimates the percentage price change for a 1% change in yield (a modified duration of 7 means roughly a 7% price drop if yields rise 1%). Because the price-yield relationship is curved rather than straight, duration alone overstates losses and understates gains for large moves; convexity is the second-order correction that captures that curvature. Together, the linear duration term plus the convexity term give an accurate estimate of price changes. The tool supports annual, semiannual, or quarterly coupons.

How it works — the formula

Price = Σ CFₜ / (1 + y/m)^t Macaulay D = [Σ t · PV(CFₜ) / Price] / m (years) Modified D = Macaulay / (1 + y/m) Convexity = [Σ t(t+1)·CFₜ/(1+y/m)^(t+2) / Price] / m²

Cash flows are discounted to price; duration is their time-weighted average; convexity is the second moment that captures price-curve bending.

Source: Investopedia — Convexity

Worked examples

Example 1
$1,000, 5% annual, 5% YTM, 10 yr
Inputs:
face=1000, coupon=5, ytm=5, years=10, freq=1
Output:
price $1,000, Mac 8.108, Mod 7.722, convexity 75.0
Example 2
$1,000, 6% annual, 5% YTM, 10 yr
Inputs:
face=1000, coupon=6, ytm=5, years=10, freq=1
Output:
price $1,077.22, Mod ~7.52
Example 3
Zero-coupon $1,000, 5% YTM, 10 yr
Inputs:
face=1000, coupon=0, ytm=5, years=10, freq=1
Output:
duration ≈ 10 (all cash at end)

Limitations

  • Flat yield curve assumed; no term-structure modeling.
  • No embedded options (callable/putable bonds need effective duration).
  • Convexity is annualized via the period-frequency adjustment.

Standard fixed-coupon analytics; not investment advice.

Frequently asked

What is the difference between Macaulay and modified duration?+
Macaulay duration is the weighted-average time to receive a bond’s cash flows, measured in years. Modified duration divides that by (1 + yield per period) and measures price sensitivity — the approximate percentage price change for a 1% change in yield.
What does convexity tell me?+
Convexity measures the curvature of the price-yield relationship. Duration assumes a straight line, but the real curve bends, so convexity corrects the estimate: it makes price gains from falling yields larger and price losses from rising yields smaller than duration alone predicts.
How do I estimate a bond’s price change?+
Use ΔP/P ≈ −(modified duration × Δyield) + ½ × convexity × (Δyield)². The first term is the linear duration effect; the second adds the convexity correction, which matters most for larger yield moves.
Why is duration in years but used as a percentage?+
Macaulay duration is genuinely a time (years). Modified duration, derived from it, happens to equal the percentage price sensitivity per 1% (100 bp) yield change. So a modified duration of 7 "years" means about a 7% price change per 1% yield move.
Does a higher coupon mean higher or lower duration?+
Lower. A higher coupon returns more of your money sooner, shortening the weighted-average time to cash flows, so duration falls. Zero-coupon bonds have the highest duration (equal to maturity) because all the cash comes at the end.
Does this handle callable bonds?+
No. It assumes plain fixed coupons with no embedded options. Callable or putable bonds need effective (option-adjusted) duration and convexity, which account for the issuer’s or holder’s right to redeem early.

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