What this calculator does
Bond duration & convexity works out how sensitive a bond’s price is to a change in yield, to first and second order. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaMacaulay duration = Σ [t·CFt/(1+i)^t] / Price; Modified duration = Macaulay / (1+i); Convexity = (P₊ + P₋ − 2P₀) / (P₀·Δy²), from prices at yield ± a small shift
The inputs explained
| Field | What to enter |
|---|---|
| Face value ($) | A number, measured in your currency. Starts at 1000. |
| Coupon rate (%) | A number, measured in %. Starts at 5. |
| Yield to maturity (%) | A number, measured in %. Starts at 6. |
| Years to maturity | A number. Starts at 10. |
| Payments per year | Choose from Annual, Semi-annual, Quarterly. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with face value
Every other input is held at the calculator’s starting values while face value varies. Select any row to load that scenario into the calculator.