Bond Duration Calculator

Calculate Macaulay and modified duration to measure interest rate sensitivity.

Please note: For information only, not investment advice. Projections assume constant rates; real markets fluctuate and capital is at risk.

What the Bond Duration Calculator does

Duration measures how sensitive a bond price is to interest rate changes. Macaulay duration is the weighted average time until you receive your money; modified duration converts that into a direct percentage price sensitivity. Longer duration means more interest rate risk.

Formula

Macaulay = Σ (t × PV of cash flow) ÷ Price
Modified = Macaulay ÷ (1 + y/f)
Price change ≈ −Modified × Δy + ½ × Convexity × Δy²

Inputs explained

Input	Unit	Required	Notes
Face (par) value	selected currency	Yes	Accepts more than 0.
Annual coupon rate	%	Yes	—
Yield to maturity	%	Yes	—
Years to maturity	number	Yes	Accepts 0 or more, up to 100.
Coupon frequency	one of 3 options	Yes	—
Currency	one of 10 options	Optional	—

How to use it

Choose Coupon frequency and Currency.
Enter Face (par) value, Annual coupon rate, Yield to maturity and Years to maturity.
Select Calculate.

Worked example

A $1,000 bond, 5% semi-annual coupon, 10 years, yielding 6%.

Face: 1000
Coupon: 5
YTM: 6
Years: 10

Macaulay duration about 7.9 years and modified duration about 7.6 — a 1% yield rise costs roughly 7.6% of the price.

Frequently asked questions

Why is duration shorter than maturity?

Because coupons return part of your money before maturity. A zero-coupon bond, which pays nothing until the end, has duration equal to its maturity.

How do I reduce interest rate risk?

Hold shorter-duration bonds. They fall less when yields rise, at the cost of a lower yield in most environments.

Method and sources

Method. Macaulay duration as the present-value-weighted average time to each cash flow, and modified duration as that figure divided by (1 + yield ÷ frequency) to give price sensitivity.

Assumptions

Yields move in parallel across all maturities, which is the assumption modified duration is built on.
Cash flows are fixed and the bond is option-free.

Limitations

Duration is a first-order estimate, accurate for small moves and increasingly wrong for large ones. Convexity is the missing second-order term, and it means real price falls less than duration predicts on a rate rise and rises more on a fall.
Yield curves rarely shift in parallel, so a duration-matched position is not the hedge it appears to be against a curve that twists.
Duration is meaningless for a bond whose cash flows can change — callable, puttable or floating — without a model of the option.

Sources

Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856 — National Bureau of Economic Research (Macaulay), 1938. The present-value-weighted average maturity that Macaulay duration measures.