Bond Convexity Calculator

Measure the curvature of a bond’s price-yield relationship that duration alone misses.

About Bond Convexity Calculator

Duration is a straight-line approximation, which understates gains when yields fall and overstates losses when they rise. Convexity is the correction term, and it always works in the bondholder’s favour for ordinary bonds. For large yield moves the convexity term matters materially, which is why long bonds gain more in a rally than duration alone predicts.

Formula

Bond Convexity

Price change % ≈ −modified duration × Δy + ½ × convexity × (Δy)²

convexity: Second-order term capturing curvature of the price-yield curve
Δy: Change in yield, in percentage points

Worked example

With the default values below, Bond Convexity Calculator returns Convexity of 57.823. Change any input above and every figure here is recalculated in your browser.

Inputs used

Face valueminimum 0.01: 1,000
Market yieldaccepts 0–100 %: 5 %
Years to maturityaccepts 0.5–50 years: 10 years
Modified durationaccepts 0.1–40 years: 7.5 years
Yield change to modelaccepts 0–100 %: 1 %

Results

Convexity: 57.823
Price Change From Duration Alone: -7.5000%
Convexity Adjustment: 0.2891%
Estimated Total Price Change: -7.2109%
Price Change in Money: -$72.11

Step by step

1Values used
2Bond Convexity
3Convexity= 57.823
4Price Change From Duration Alone= -7.5000
5Convexity Adjustment= 0.2891
6Estimated Total Price Change= -7.2109
7Price Change in Money= -72.11

Assumptions and limits

The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Bond Convexity calculated?

Price change % ≈ −modified duration × Δy + ½ × convexity × (Δy)² Duration is a straight-line approximation, which understates gains when yields fall and overstates losses when they rise. Convexity is the correction term, and it always works in the bondholder’s favour for ordinary bonds.

Why does Bond Convexity matter?

For large yield moves the convexity term matters materially, which is why long bonds gain more in a rally than duration alone predicts.

What values do I need to enter?

This calculator takes 5 inputs: Face value, Market yield, Years to maturity, Modified duration, Yield change to model. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.