Bond Duration and Convexity Calculator
Measure fixed-coupon bond interest-rate sensitivity and compare duration/convexity approximation with exact repricing.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Weight payment times by discounted cash flows for Macaulay duration, adjust for compounding for modified duration and calculate the second price derivative for convexity.
Modified duration=Macaulay/(1+y/f); ΔP/P≈−Dmod×Δy+0.5×convexity×Δy²
Worked example
A one-year zero-coupon bond at 0% yield has Macaulay duration 1, modified duration 1 and annual-frequency convexity 2.
Assumptions and input details
Same coupon-date and fixed promised cash-flow assumptions as Bond Price and Yield. Convexity uses annual-yield derivatives, with units years². Shock is an absolute percentage-point change, not a relative percent of yield. Approximation can be poor or negative for large shocks; exact repricing uses the same unchanged cash flows, not credit/spread or option changes. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: FINRA: duration and rate changes
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Price a fixed-coupon bond at a coupon date or solve its yield from an entered full price.
Derive the implied forward rate between two entered effective annual spot rates and maturities.
Add balances in different currencies, including debts. Convert the total and compare a table and currency chart.
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