Bond Duration Calculator (Macaulay + Modified)
Bond duration calculator. Macaulay + modified duration from face value, coupon, maturity, and YTM. Measures interest-rate sensitivity.
Bond Duration Calculator
Computes a bond's Macaulay duration (the weighted-average time to receive its cash flows, in years) and modified duration (the % price change for a 1% move in yield) from its coupon, maturity, and yield to maturity. Duration is the standard first-order measure of a bond's interest-rate risk.
How to Use the Bond Duration Calculator
Enter the bond's terms
Face value (usually $1,000), the annual coupon rate, and years to maturity. These define the cash flows the bond will pay.
Enter the yield to maturity
YTM is the market discount rate — the return a buyer earns holding to maturity. It drives both price and duration. Use the current market yield, not the coupon.
Set coupon frequency
Most US corporate and Treasury bonds pay semi-annually; some pay annually or quarterly. Frequency affects the period count and the per-period discounting.
Read duration as risk
Modified duration tells you the approximate % the price moves for a 1% yield change. A duration of 8 means a 1% yield rise costs roughly 8% of price — the headline interest-rate risk number.
Understanding Bond Duration
Macaulay vs Modified Duration
Macaulay duration, introduced by Frederick Macaulay in 1938, is the weighted-average time (in years) until a bondholder receives the bond's cash flows, weighting each payment by its present value. Modified duration rescales it into a price-sensitivity measure: divide Macaulay duration by (1 + yield/frequency) and you get the approximate percentage change in price for a 1-percentage-point change in yield. A modified duration of 8 means roughly an 8% price drop if yields rise 1% — and an 8% gain if they fall 1%.
Why Duration Matters
Duration is the single most important risk number in fixed income. It lets a portfolio manager compare the interest-rate risk of bonds with wildly different coupons and maturities on one scale, immunize a portfolio against rate moves, and estimate gains and losses before they happen. Longer maturity, lower coupon, and lower yield all push duration up — making a bond more rate-sensitive.
"A zero-coupon bond's Macaulay duration equals its maturity exactly — there's only one cash flow. Every coupon a bond pays before maturity pulls its duration below its maturity."
The Limits of Duration
Duration is a first-order (linear) approximation. For small yield moves it's accurate; for large moves it overstates losses and understates gains, because the price-yield relationship is curved, not straight. That curvature is convexity — the second-order correction. For big rate scenarios, pair this calculator with our Bond Convexity Calculator to refine the estimate.
10 Facts About Bond Duration
Macaulay duration was defined by Frederick Macaulay in 1938 — the formula hasn't changed since.
A zero-coupon bond's duration equals its maturity exactly.
Modified duration ≈ the % price move for a 1% yield change.
Lower coupon → higher duration → more interest-rate risk.
Longer maturity → higher duration, but the relationship isn't perfectly linear.
Higher yield → lower duration (near-term cash flows weigh more).
DV01 ("dollar value of 1 basis point") is duration expressed in dollars per 0.01% yield move.
Duration immunization matches asset and liability durations to neutralize rate risk.
Duration is a linear approximation; convexity is the second-order correction.
A bond fund's quoted "duration" is the weighted average of its holdings' durations.
Frequently Asked Questions
- Macaulay duration is the weighted-average time (in years) to receive a bond's cash flows. Modified duration rescales it into price sensitivity: Macaulay ÷ (1 + yield/frequency). Modified duration tells you the approximate percentage price change for a 1-percentage-point change in yield, so it's the number traders use for risk.
- Use the current market yield for a bond of similar credit quality and maturity — not the coupon rate. YTM is the discount rate that makes the present value of the cash flows equal the market price. If you only know the price, our other tools can help; here, enter the prevailing market yield.
- Duration weights each cash flow by its present value and timing. A low-coupon bond pays less along the way, so more of its value comes from the distant face-value payment — pushing the weighted-average time (and rate sensitivity) up. A zero-coupon bond is the extreme: its duration equals its full maturity.
- DV01 — "dollar value of 1 basis point" — is the dollar change in a bond's price for a 0.01% (1 basis point) change in yield. It's duration expressed in money rather than percent, which is how desks size and hedge positions. This tool reports it alongside duration.
- Very accurate for small yield moves (under ~0.25%). For larger moves, duration alone overstates losses and understates gains because the true price-yield curve bends — duration is a straight-line approximation to it. Add convexity (our companion calculator) to correct for big moves.
- Yes. Frequency sets how many periods exist and how the yield is compounded per period. Most US Treasury and corporate bonds pay semi-annually — the default here. Switching to annual or quarterly shifts both price and duration slightly because the timing of cash flows changes.
- A bond trades at a premium when its price is above par (face) — which happens when its coupon exceeds the market yield. It trades at a discount when the price is below par (coupon below market yield), and at par when coupon equals yield. The tool labels which case your inputs produce.
- This calculator models a single bond. A fund's duration is the value-weighted average of its holdings' durations — the figure the fund publishes in its fact sheet. You can sanity-check a fund's reported duration against a representative bond here, but for the fund's exact number use its disclosed duration.
- No — except for a zero-coupon bond, where they're equal. For a coupon bond, duration is always less than maturity because some value is returned along the way via coupons. The bigger the coupon, the more duration falls below maturity.
- Managers use duration to position for rate views and to immunize liabilities. If you expect rates to rise, you shorten duration to cut losses; if you expect them to fall, you extend it to capture gains. Pension funds match the duration of assets to liabilities so that a rate move changes both by the same amount, neutralizing the impact. Duration is the dial they turn to set interest-rate exposure.
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Method & sources
How it computes
Each coupon and the final principal repayment is discounted at the yield to maturity to give the bond price. Macaulay duration is the present-value-weighted average time to those cash flows, measured in years: the sum of (time x present value) divided by the price. Modified duration is the Macaulay figure divided by (1 + yield per period), and estimates the percentage price change for a one-point move in yield. Coupon frequency sets both the period count and the per-period yield.
What this tool implements
- Macaulay duration is reported in YEARS, not coupon periods — the weighting uses t/f, so a semiannual bond does not report a figure twice its true duration.
- Modified duration divides by (1 + y/f), using the periodic yield rather than the annual one. Dividing by (1 + y) instead is a common error that understates the sensitivity of any bond paying more often than annually.
- Verified 2026-08-31 by the zero-coupon identity, which is the check that actually binds: a zero has all its value in one cash flow, so its Macaulay duration must equal its maturity exactly. A 10-year zero returns 10.000000.
- ⚠️ A single flat yield discounts every cash flow. Real curves slope, so a bond priced off a steep curve will have a duration that differs from this figure; and the calculation assumes option-free cash flows — for a callable, putable or mortgage-backed bond, where the cash flows themselves move with yields, effective duration is the right measure and this is not it.
Sources
- Macaulay FR. 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, 1938 — the paper that introduced the measure: https://www.nber.org/books/maca38-1
- Fabozzi FJ. Bond Markets, Analysis, and Strategies — the standard reference for the Macaulay/modified relationship and for why effective duration replaces modified duration once a bond has embedded options.
What can make this go out of date
- Nothing is fetched and no market data is consulted. Every figure comes from the four inputs, so the output is only as current as the yield the user supplies.
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