Bond Duration and Convexity Calculator
Macaulay and modified duration plus convexity, summed from the actual cash flows, with what a one-point rate move does to the price.
Results
What this tool does
Duration says how far away a bond's money really is, once you weigh each payment by its present value — and that single number is also, almost exactly, how much the price falls for each point that yields rise. Almost. The relationship is a curve, not a straight line, and duration is only the tangent to it. Convexity measures the bend, and it always works in the bondholder's favour: prices rise more than duration predicts when yields fall, and drop less than it predicts when they rise. This page computes both by summing the actual cash flows, and shows what each one contributes to a one-point move.
Formula
D = Σ t × PV(flow_t) ÷ price · convexity = Σ t(t+1) flow_t ÷ (1+y)^(t+2) ÷ price, summed cash flow by cash flow
Variables
| Symbol | Meaning | Unit |
|---|---|---|
face | Face value | — |
coupon | Coupon rate | % |
yield_rate | Yield to maturity | % |
years | Years to maturity | — |
freq | Coupons per year | — |
DU | Macaulay duration | — |
DM | Modified duration | — |
CX | Convexity | — |
PR | Bond price | — |
D1 | Price change if rates rise one point | — |
PA | Price after that rise | — |
LO | What duration alone would predict | — |
CG | What convexity gives back | — |
DV | Money lost per basis point | — |
MP | Duration counted in periods | — |
PY | Yield per period | % |
NP | Periods | — |
Worked example
- Face value100
- Coupon rate5 %
- Yield to maturity4 %
- Years to maturity10
- Coupons per year1
- Macaulay duration8.190899
- Modified duration7.875864
- Convexity77.482001
- Bond price108.110896
- Price change if rates rise one point-8.095835
- Price after that rise100.015061
- What duration alone would predict-8.514667
- What convexity gives back0.418832
- Money lost per basis point0.085147
- Duration counted in periods8.190899
- Yield per period4.000000 %
- Periods10
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.
Frequently asked questions
What is the difference between Macaulay and modified duration?
Macaulay duration is a time: the weighted average number of years until you get your money back, weighting each payment by its present value. Modified duration is that number divided by one plus the yield, and it is a sensitivity: it estimates the percentage price change for a one percentage point move in yield. For large moves the estimate is too pessimistic, because the price-yield curve bends — that curvature is convexity.