Bond duration calculator

Published August 16, 2026

Macaulay duration is the present-value-weighted time until a bond's cash flows arrive. A 5-year 5 percent annual coupon bond at a 5 percent yield, priced at par of $1,000, has a Macaulay duration of 4.55 years, a modified duration of 4.33 years, and a DV01 of $0.43.

Macaulay duration

4.55 years

Modified duration 4.33 years. A one basis point fall in yield lifts the price by about $0.43.

Price: $1,000.00
Coupon each period: $50.00
Macaulay duration: 4.55 years
Modified duration: 4.33 years
DV01: $0.43

Face value

Coupon rate

Annual coupon as a percent of face. Paid in equal instalments at the frequency below.

Yield to maturity

Years to maturity

Payments a year

The formula

D_{Mac} = \frac{\sum_t t \, PV(CF_t)}{P} \qquad D_{Mod} = \frac{D_{Mac}}{1 + y/k}

$PV(CF_t)$ is the present value of the cash flow at time $t$ in years, $P$ the price, $y$ the annual yield and $k$ the number of coupon periods a year. DV01 is modified duration times price over 10,000: the dollar change for a one basis point fall in yield.

Duration is a weighted average wait

A bond pays coupons along the way and face at the end. Macaulay duration is the average of those dates, each weighted by the present value of that cash flow. A 5-year annual 5 percent coupon bond at a 5 percent yield is worth par, $1,000, and its Macaulay duration is 4.55 years, not 5, because some of the value arrives as coupons before maturity.

At par the coupons and the yield match, so the weights are easy to see: each $50 coupon is discounted at 5 percent, and the $1,000 face at year 5 is discounted at 5 percent. Pull some of the weight forward into the coupons and the average date lands before maturity. A zero-coupon bond has no coupons to pull, so its Macaulay duration equals its maturity.

The unit is years. Saying a bond 'has duration 4.55' without the unit is how it gets mixed up with modified duration, which is also in years but answers a different question.

Modified duration is the price sensitivity

Macaulay duration is a wait. Modified duration is that wait adjusted for compounding, $D_{Mac} / (1 + y/k)$ , and it is the percent the price moves when the yield moves by 1 percentage point, for a small move. On the par bond, modified duration is 4.33 years, so a 1 percentage point fall in yield raises the price by about 4.33 percent. DV01 scales that to one basis point: $0.43.

The approximation is linear. Convexity, which this page does not compute, says the actual price rise on a fall in yield is a little larger than modified duration predicts, and the actual fall on a rise in yield is a little smaller. For a one-basis-point move the difference is noise. For a one-percentage-point move it is visible.

A 10-year 6 percent coupon bond with semiannual coupons, at a 5 percent yield, prices at $1,077.95, a premium. Macaulay duration is 7.76 years, modified duration 7.57 years, DV01 $0.82. Premium bonds have shorter duration than par bonds of the same maturity, because more of the value sits in the coupons.

What duration is for, and what it is not

Duration is how you compare two bonds that do not share a maturity, or a bond with a portfolio, on interest-rate risk. It is not a forecast of what yields will do, and it is not a measure of credit risk. A 4.55-year duration bond can still default tomorrow.

It is also not a hold-to-maturity return. Yield to maturity already answers that, on the assumption coupons are reinvested at the yield. Duration answers a different question: if the yield changes now, how far does the price move now. The bond price calculator is the price identity; this page is the sensitivity of that identity.

Immunisation, matching duration to a liability date, uses Macaulay duration. Hedge ratios use modified duration. Mixing the two is how a hedge comes out 5 percent too large or too small, which is the $1 + y/k$ factor you skipped.

Frequency has to match the market's convention

US Treasuries and most US corporates pay semiannually. Annual coupons are the teaching case because the numbers stay clean. The formula does not care, as long as $k$ , the coupon rate, and the yield all describe the same period. A 5 percent annual yield on a semiannual bond is 2.50 percent a half-year, not 5 percent a half-year.

The APR against APY calculator is the conversion if you have been given an effective annual yield and need a nominal one to split across $k$ . Bond yields in the US are usually quoted as nominal, twice a year, which is already the $y$ this formula wants for $k = 2$ .

Worked examples

A 5-year par bond, annual coupons

Face $1,000, 5 percent annual coupon, 5 percent yield, 5 years, annual payments. Price, Macaulay duration, modified duration, DV01?

Each coupon is $1000 \times 0.05 = 50$ , so $50. At a 5 percent yield the bond is at par: price $1,000.
Macaulay duration, the present-value-weighted wait, is 4.55 years.
Modified duration: $4.55 / 1.05 = 4.33$ years.
DV01: $4.33 \times 1000 / 10000 = 0.43$ , so $0.43 per basis point.

The bond prices at $1,000. Macaulay duration is 4.55 years, modified duration 4.33 years, and DV01 is $0.43. Coupon each year is $50.

A 10-year premium bond, semiannual coupons

Face $1,000, 6 percent coupon, 5 percent yield, 10 years, two payments a year. Price and duration?

Coupon each half-year: $1000 \times 0.06 / 2 = 30$ , so $30.
Price, discounting 20 coupons and the face at 2.50 percent a half-year: $1,077.95.
Macaulay duration 7.76 years, modified duration 7.57 years, DV01 $0.82.

The bond prices at $1,077.95, a premium because the coupon sits above the yield. Macaulay duration is 7.76 years, modified duration 7.57 years, DV01 $0.82. Each half-year coupon is $30.

A zero-coupon 5-year bond at 5 percent

Face $1,000, coupon 0, yield 5 percent, 5 years, annual. Confirm Macaulay duration equals maturity.

Price is $1000 / 1.05^{5} = 783.53$ .
The only cash flow is at year 5, so Macaulay duration is 5.00 years.
Modified duration: $5 / 1.05 = 4.76$ years. DV01: $4.76 \times 783.53 / 10000 = 0.37$ .

Price $783.53. Macaulay duration is 5.00 years, equal to maturity, because nothing arrives before then. Modified duration is 4.76 years and DV01 is $0.37. The coupon each period is $0.

The mistake that costs the most

Using Macaulay duration as a hedge ratio, or modified duration as a wait.

Macaulay 4.55 years is when the cash flows arrive, on average, in present-value terms. Modified 4.33 is how far the price moves. A hedge that needs 'how far the price moves' and is built on 4.55 is 5 percent too large, which is exactly the $1.05$ factor on this par bond. Write down which one you mean. The names exist because the two numbers are not interchangeable.

Common questions

Why is duration shorter than maturity?

Because some of the value arrives as coupons before the face is paid. Only a zero-coupon bond has duration equal to maturity. Higher coupons and higher yields both pull duration in, because they put more weight on the earlier cash flows.

Is DV01 the same as duration?

No. DV01 is the dollar change in price for a one basis point move, which is modified duration times price over 10,000. Duration is a time or a percent. DV01 is money.

Does duration measure default risk?

No. It measures interest-rate sensitivity of a promised cash-flow schedule. A high-yield bond can have a short duration and a high chance of default at the same time.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.