The bond duration calculator above prices a plain fixed-coupon bond from its own cash flows and then measures how sensitive that price is to a change in yield. It reports all three duration figures that appear on a fixed-income screen — Macaulay, modified and effective — along with convexity, and it shows the price change the standard second-order approximation predicts for whatever yield shift you enter. The formulas are the published ones and nothing is hardcoded: coupon, maturity, yield and payment frequency are all yours to set.
Arb Digital publishes free finance calculators that show their working rather than a single unexplained number. Duration is worth that treatment because the word is genuinely ambiguous. It is quoted in years, it comes in several flavours that give different answers for the same bond, and the most common everyday reading of it — how long until I get my money back — is not what any of the three measures actually means.
What This Bond Duration Calculator Does
You supply the bond's terms and its current yield to maturity. The tool builds the full schedule of coupon payments plus the final return of face value, discounts every one of them at the per-period yield, and adds them up to get a price. That price is the base for everything else on the page.
Macaulay duration is the present-value-weighted average time to receive the bond's cash flows, expressed in years. Modified duration divides that by one plus the per-period yield and is the figure that actually estimates a percentage price change per unit of yield change. Effective duration is computed differently: the tool reprices the bond at a yield above and below the current one and measures the slope numerically, which is the method that survives when cash flows are not fixed. Convexity measures how much the price-yield relationship curves, and it is the correction that makes a large yield move estimate usable.
This page assumes a plain bond with fixed coupons and no embedded options. It sits alongside the bond price calculator, which values the bond, and the yield to maturity calculator, which solves for the yield from a price. Those two answer what a bond is worth; this one answers how much that worth moves when rates move. If your bond is callable, the issuer's option changes the cash flows entirely and the yield to call calculator is the right starting point instead.
How to Use It
- Enter the face value and coupon rate from the bond's own terms. Both are fixed at issue. The coupon rate is a percentage of face value per year, not of the price you paid.
- Enter the remaining years to maturity, not the original term. A thirty-year bond issued twenty years ago has ten years left, and duration depends only on what is still to come.
- Take the yield to maturity from a live quote. Yields move daily. Use your broker's figure or derive it from today's price; a stale yield produces a stale duration.
- Set the payment frequency to match the bond. Most corporate and government bonds pay semi-annually. Frequency changes both the price and the duration, sometimes by more than people expect.
- Choose a yield shift and read the estimated price change. Start with 100 basis points, then try 300 to see how far the linear duration estimate drifts from the convexity-corrected one.
How Duration Is Calculated
Write i for the yield per period, so a 6 per cent annual yield paid semi-annually gives i = 0.03, and n for the number of periods remaining. Each cash flow Ck is discounted to a present value of Ck ÷ (1 + i)k, and the price is the sum of those. Macaulay duration in periods is the weighted average of k using those present values as weights; divide by the number of periods per year to get years. Modified duration is Macaulay duration divided by (1 + i).
Work the default through. A bond with 1,000 face value, a 5 per cent coupon paid semi-annually, ten years remaining and a 6 per cent yield has twenty periods, a coupon of 25 per period and a per-period yield of 3 per cent. The annuity factor for twenty periods at 3 per cent is 14.8775, so the coupons are worth 371.94, and the face value discounts to 553.68. The price is 925.61 — a discount to par, as it must be when the coupon is below the yield. Weighting each period by its present value gives a Macaulay duration of about 7.89 years, and dividing by 1.03 gives a modified duration of about 7.66.
Read that modified duration as a slope. A one percentage point rise in yield is estimated to cut the price by roughly 7.66 per cent, and a one point fall to raise it by roughly the same. Convexity then corrects the estimate: the true price-yield curve bends upward, so the first-order estimate overstates the loss on a rate rise and understates the gain on a rate fall. The full approximation is a percentage price change of minus modified duration times the yield change, plus one half of convexity times the yield change squared. FINRA's investor page on bonds covers interest rate risk and duration risk in plain language, and is a good companion to the arithmetic here.
Duration Is Not a Time Horizon
This is the misreading that causes real confusion, and it is worth stating flatly. Macaulay duration does have units of years and it does have a genuine interpretation as an average time — the present-value-weighted average of when the money arrives. But modified and effective duration, the two figures actually used to manage risk, are sensitivities that happen to inherit those units. A modified duration of 7.66 is not a prediction that anything happens in 7.66 years. It is a statement about percentage price change per percentage point of yield.
The one place the time reading has a legitimate use is immunisation. If a portfolio's Macaulay duration matches an investor's horizon, the loss of price from a rate rise is offset to first order by the higher reinvestment rate on the coupons, so the value at that horizon is roughly insulated from a small parallel rate move. That is a specific, narrow, first-order result with a long list of conditions attached, and it is the exception rather than the everyday meaning.
The everyday meaning is risk. Two bonds of the same maturity can have very different durations, because a high coupon returns money sooner and shortens the weighted average, while a zero-coupon bond returns everything at the end and has a Macaulay duration exactly equal to its maturity. That is why a long, low-coupon bond is the most rate-sensitive instrument in a conventional portfolio, and it is what the second preset above demonstrates.
Why Convexity Matters and Where the Estimate Breaks
Duration is the first derivative of price with respect to yield; convexity is the second. Alone, duration describes a straight line tangent to a curve. The real relationship between a bond's price and its yield is not straight — it bends, and it bends in the holder's favour, because prices rise more on a rate fall than they drop on an equal rate rise.
For small moves this barely matters. For a 25 basis point shift the duration-only estimate is close enough for most purposes. For a 300 basis point shift it can be materially wrong, and the convexity term is doing real work. The tool shows both the duration-only figure and the convexity-corrected one so the gap is visible rather than assumed away.
Two further limits deserve stating. First, both estimates assume a parallel shift in the yield curve — every maturity moving by the same amount. Real curves twist, steepen and flatten, and a portfolio can be duration-neutral and still lose money on a curve reshape. Second, neither figure says anything about credit. A corporate bond's price can fall while government yields are unchanged, simply because the market has repriced the issuer's chance of paying. The SEC's investor education pages on bonds list credit risk, call risk and liquidity risk alongside interest rate risk, and none of the others appear anywhere in a duration number.
Effective Duration and Why It Exists
Modified duration is a closed-form result that assumes the cash flows are fixed. The moment a bond has an embedded option that assumption fails. A callable bond's issuer will redeem early if rates fall far enough, so the cash flows themselves depend on the yield, and differentiating a formula that treats them as constant gives an answer for a bond that does not exist.
Effective duration sidesteps this by measuring rather than deriving. It reprices the bond at a yield slightly above and slightly below the current level and takes the slope between the two prices. For the plain bond modelled here, effective duration comes out almost identical to modified duration, and the small difference you can see between the two boxes is the curvature captured by using a finite shift instead of an infinitesimal one. That agreement is a useful sanity check on the arithmetic.
For a callable or putable bond the two diverge sharply, and effective duration is the one that means anything. A callable bond's effective duration shortens as rates fall, because the call becomes more likely and the expected life collapses. That behaviour — negative convexity — is why callable bonds participate less in a rally than their stated maturity suggests. This page does not model embedded options and does not try to; it reports effective duration for the fixed cash flows you entered, which is a numerical measurement of exactly that bond and nothing more.
What Changes Duration
Four inputs move duration, and knowing the direction of each is more useful than memorising a number. Longer maturity raises duration, though at a decreasing rate — the difference between a five-year and a ten-year bond is far larger than the difference between a twenty-five-year and a thirty-year one, because the far-off cash flows are heavily discounted and carry little weight.
A higher coupon lowers duration, since more of the value arrives early. A higher yield also lowers duration, because a higher discount rate shrinks distant cash flows more than near ones and shifts the weighted average forward. This last effect is why duration is not a fixed property of a bond: the same security has a different duration at a 3 per cent yield than at an 8 per cent one, and any duration figure is only valid at the yield it was computed for.
More frequent coupons lower duration slightly, for the same reason a higher coupon does. Together these explain why a portfolio's rate sensitivity drifts over time even when nothing is bought or sold, and why duration has to be recomputed rather than remembered. If you are comparing this measure against other portfolio statistics, the Sharpe ratio calculator and the portfolio rebalancing calculator cover different dimensions of the same question.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Reading duration as a waiting time — modified and effective duration are price sensitivities in units of years, not a date on which anything happens.
- Using a duration computed at a different yield — duration changes as yields change, so a figure from last quarter describes a bond that no longer exists at today's price.
- Applying duration to a large yield move without convexity — the linear estimate drifts badly beyond about a percentage point, always in the direction of overstating losses.
- Assuming a parallel curve shift — real yield curves twist and steepen, and a duration-matched position can still lose money when the shape changes rather than the level.
- Treating duration as a measure of total risk — credit, liquidity and call risk are entirely absent from it, and for a corporate bond they can dominate.
Related Free Tools From Arb Digital
Price the bond itself with the bond price calculator, solve for its yield with the yield to maturity calculator or the bond yield calculator, and handle the issuer's early redemption option with the yield to call calculator. For the discounting arithmetic underneath all of it, the present value calculator and the NPV calculator are useful, and the inflation calculator puts a nominal yield into real terms. Every free tool Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Macaulay duration is the present-value-weighted average time until a bond's cash flows arrive. Modified duration is that figure divided by one plus the per-period yield, and it is the one that estimates the percentage price change for a change in yield.
No. Only Macaulay duration has an average-time reading, and even then it is a weighted average rather than a payback date. Modified and effective duration are sensitivity measures that inherit the unit of years without inheriting the meaning.
Effective duration is measured by repricing the bond at yields above and below the current one, so it captures a little of the curvature over that finite shift. For a plain fixed-coupon bond the two figures should be very close, and a large gap would point to an input error.
Convexity is the curvature of the price-yield relationship. Duration alone draws a straight line, which underestimates gains when yields fall and overestimates losses when they rise. The convexity term corrects the estimate, and matters most for large yield moves.
Because there is only one cash flow, so the weighted average time to receive the money is the maturity date itself. That also makes zero-coupon bonds the most rate-sensitive bonds of any given maturity.
No. Duration measures sensitivity to interest rates only. Credit risk, liquidity risk and call risk are separate and are not reflected anywhere in the calculation on this page.
Not properly. A callable bond's cash flows change with the level of rates, which requires an option-adjusted model. This page assumes fixed coupons, so its output describes a non-callable bond with the terms you entered.
A higher discount rate shrinks distant cash flows more than near ones, which pulls the weighted average time forward. Duration is therefore a property of a bond at a particular yield, not a permanent characteristic of the security.
This tool is provided for information and education only and is not investment advice, a recommendation, or a price target. It applies a standard fixed-cash-flow duration model, assumes a parallel shift in the yield curve, and ignores credit, liquidity, tax and embedded-option effects. Speak to a licensed financial adviser before making any investment decision.
