Bond Duration Calculator
Macaulay and modified duration and convexity of a fixed-coupon bond from its coupon, yield, term and payment frequency, and the price change for a yield move: estimated by duration, by duration plus convexity, and repriced exactly.
Result…
How it's calculated
Price P = Σ CFₜ ÷ (1 + y)ᵗ, with y = yield ÷ payments a year (k) Macaulay duration = Σ (t ÷ k) × CFₜ ÷ (1 + y)ᵗ ÷ P Modified duration = Macaulay ÷ (1 + y) Convexity = Σ CFₜ × t(t + 1) ÷ (1 + y)ᵗ⁺² ÷ (P × k²) % price change ≈ −modified × Δy + ½ × convexity × Δy²
Duration measures how sensitive a bond's price is to a change in interest rates. Macaulay duration is the weighted average time, in years, until the bond's cash flows are received, each weighted by its present value. Modified duration turns that into a price sensitivity: a modified duration of 7 means the price falls about 7% when the yield rises by one percentage point. Because the price-yield curve bends, duration alone overstates falls and understates rises; convexity corrects most of that gap. This calculator builds the bond's cash flows from your coupon, yield, term and frequency, works out all three measures step by step, and compares the two estimates with the exact price at the new yield, so you can see how good the approximation is. See also the bond yield calculator.
Your numbers, step by step
About the Bond Duration calculator
This bond duration calculator measures how sensitive a fixed-coupon bond is to interest rates. From the face value, coupon rate, yield to maturity, years to maturity and payments a year, it builds every cash flow and works out the Macaulay duration (the present-value-weighted average time to the cash flows, in years), the modified duration (the percentage price change for a one-point move in yield) and the convexity. It then takes a yield change you choose in basis points and shows three answers: the price change estimated by duration alone, the estimate with convexity added, and the exact change from repricing the bond. Students can check textbook answers, and investors can see how much a rate move could change a bond's price. The definitions follow the standard ones set out under duration in finance. For the yield itself, use the bond yield calculator.
How to use it
- Enter the “Face value”, the “Coupon rate (a year)” and the “Yield to maturity (a year)”.
- Enter the “Years to maturity” and choose the “Coupon payments a year”; years × payments must be a whole number.
- Set the “Yield change” in basis points (100 bp = 1 percentage point), with a minus sign for a fall.
- Read the Macaulay and modified duration, then compare the estimated and exact price changes.
Worked example
A bond with a face value of 1,000 pays a 4% coupon half-yearly, has 8 years to maturity and yields 5%. That is 16 payments of 20 plus 1,000 at the end, discounted at 2.5% a period, so the price is 934.72. The Macaulay duration is 6.8794 years and the modified duration is 6.8794 ÷ 1.025 = 6.7116; the convexity is 52.8048. If the yield rises by 100 bp to 6%, duration estimates a fall of 6.7116%, duration plus convexity a fall of 6.4476%, and repricing gives an exact fall of 6.4549%, to 874.39.
Updated
Questions people ask
What is the difference between Macaulay and modified duration?
Macaulay duration is a time, the weighted average number of years until you receive the bond's cash. Modified duration is a sensitivity: Macaulay duration ÷ (1 + yield per period), which gives the approximate percentage price change for a one percentage point change in yield.
What is the formula for a bond's price change using duration and convexity?
Percentage price change ≈ −modified duration × Δy + ½ × convexity × Δy², with Δy as a decimal (100 bp = 0.01). The convexity term is always positive for a plain bond, so it makes falls smaller and rises larger than duration alone suggests.
Why is the duration of a zero-coupon bond equal to its maturity?
A zero-coupon bond has only one cash flow, at maturity, so all the weight sits on that date. Its Macaulay duration is therefore exactly the years to maturity; coupon bonds have shorter durations because some cash arrives earlier.
What is a common mistake when using duration?
Applying it to large yield moves. Duration is a straight-line estimate of a curved price-yield relationship, so for moves of 100 bp or more the error grows; add convexity or compare with the exact repriced change the calculator shows.
Does this work for callable bonds or prices between coupon dates?
No. It assumes a plain fixed-coupon bond priced on a coupon date, with no calls, puts or default. Bonds with options need effective duration from a pricing model, and markets apply their own day-count and accrued interest rules; a financial professional can help with those.