Effective Duration Calculator
Effective duration measures how much a bond’s price should move when yields shift, using prices that already reflect any change in the bond’s expected cash flows. That makes it the right risk number for callable bonds, putable bonds, and mortgage-backed securities, where cash flows move with rates. This calculator takes the three prices from a repricing exercise, the price if yields fall, the price if yields rise, and the current price, plus the size of the yield shift, and returns the duration. One boundary to know up front: it does not reprice the bond for you. The two shifted prices come from your pricing model, spreadsheet, or data vendor, and the section below explains how to get them.
Quick Answer
A bond priced at 1,000 that reprices to 1,025 when yields fall by one point and 976 when yields rise by one point has an effective duration of 2.4500. Read that as: a further one-point rise in yields should cost the bond roughly 2.45% of its price, and a one-point fall should add roughly 2.45%, before convexity adjusts the real move.
Key takeaways
- Effective duration is computed from repriced bond values, not from the coupon schedule. If the shifted prices do not let cash flows change, the result is just modified duration in disguise.
- The yield shift goes in as a decimal: 0.01, not 1 and not 100. This is the single most common way this calculation goes wrong, and it throws the answer out by a factor of 100.
- Use the same shift, the same price basis, and full prices (including accrued interest) for all three inputs.
- Callable bonds show shorter effective duration than identical non-callable bonds, because the call caps the price gain when yields fall.
- Quick Answer
- How to use the effective duration calculator
- The effective duration formula and the repricing method behind it
- Worked example: a callable bond repriced one point each way
- Effective vs modified vs Macaulay duration: which one should you use?
- Reading the result: how much sensitivity is a lot?
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the effective duration calculator
You need three prices and one shift size. The prices are the part most people get stuck on, so start there.
- Get the current price (P0): the bond’s full price today. If your source quotes a clean price, add accrued interest so all three prices share the full-price basis; the settlement maths behind that sits in the bond settlement date calculator.
- Reprice the bond twice: shift the benchmark yield curve down by your chosen amount and reprice the bond with a model that allows the call, put, or prepayment behaviour to respond. That gives P−. Shift the curve up by the same amount and reprice again for P+. A spreadsheet that holds cash flows fixed cannot do this step honestly for an option-embedded bond.
- Enter the shift as a decimal: the same shift used in both repricings. One percentage point is 0.01, half a point is 0.005, 25 basis points is 0.0025.
- Click Calculate: the result is in years, like every duration measure, and the two extra lines translate it into the approximate price move for a one-point shift either way.
The effective duration formula and the repricing method behind it
Effective duration is a central-difference estimate of price sensitivity: reprice up, reprice down, and divide the price gap by the size of the round trip.
P− = full price if the yield curve shifts down by ΔY
P+ = full price if the yield curve shifts up by ΔY
P0 = current full price
ΔY = the shift, as a decimal (0.01 = 1 percentage point = 100 basis points)
Two method points decide whether the number means anything. First, the shift is a parallel shift of the benchmark yield curve, not a change in the bond’s own yield to maturity: the CFA Institute treatment of effective duration and convexity for option-embedded bonds, summarised in the AnalystPrep CFA Level I study notes, frames it exactly that way, because a callable bond may not even have a meaningful single yield to maturity. Second, there is no official bump size written into the formula. This tool applies no repricing of its own and imposes no bump: whatever shift produced your two prices is the shift you enter. In professional practice, shifts of 25 to 100 basis points are common. Very small shifts make the result jumpy when prices are rounded; very large shifts blend curvature into what is supposed to be a straight-line measure.
Worked example: a callable bond repriced one point each way
A callable corporate bond trades at a full price of 1,000. Your pricing model, with the call switched on, reprices it at 1,025 if the curve falls by one point and 976 if the curve rises by one point. The call is doing visible work here: the price gains only 25 on the way down, because the issuer is more likely to redeem the bond, but loses 24 on the way up.
| Input | Value | Meaning |
|---|---|---|
| P− (yields down 1 point) | 1,025 | Gain capped by the call option |
| P+ (yields up 1 point) | 976 | Full downside of the rate rise |
| P0 (current price) | 1,000 | Full price today |
| ΔY | 0.01 | One percentage point, as a decimal |
| Effective duration | 2.4500 | (1,025 − 976) ÷ (2 × 1,000 × 0.01) = 49 ÷ 20 |
Sanity-check the answer before you use it: the average price move across the two repricings is (25 + 24) ÷ 2 = 24.50 on a 1,000 price, which is 2.45% for a one-point shift. That is the duration, read directly. If your computed duration and that rough check disagree, an input is wrong, usually the decimal. The book value a bond is carried at on a balance sheet is a separate question, covered by the bond carrying value calculator, and it plays no part in this risk measure.
Effective vs modified vs Macaulay duration: which one should you use?
All three are stated in years and all three describe interest rate sensitivity, but they are built on different assumptions about cash flows. Picking the wrong one is not a rounding issue; for a callable bond, modified duration can overstate the upside so badly that a hedge built on it fails exactly when rates fall.
| Measure | How it is built | Cash flows assumed | Use it for |
|---|---|---|---|
| Macaulay duration | Present-value weighted average time to receive the cash flows | Fixed | Horizon matching and immunisation maths |
| Modified duration | Macaulay duration divided by (1 + yield per period) | Fixed | Option-free bonds: Treasuries, plain corporate bonds |
| Effective duration | Price change across two repricings of a shifted curve (this page) | Allowed to change as rates move | Callable and putable bonds, mortgage-backed securities, any bond with contingent cash flows |
The XplainD guide to bond duration walks through all three measures with the same framing used here, and the Handbook of Finance chapter on effective duration and convexity, available through O’Reilly’s Handbook of Finance chapter on effective duration, makes the case that the numerical (effective) approach is the more complete risk measure once optionality exists. Do not confuse any of this with a duration coefficient calculator, which answers a different question in project and engineering contexts. And once duration has told you the risk, the return side still needs its tax check, which is what an after-tax yield calculator is for.
Reading the result: how much sensitivity is a lot?
Duration bands are a rough guide, not a rating. A short Treasury bill sits near zero; a long zero-coupon bond can run into the teens or higher. These bands describe typical investment-grade bond territory.
| Effective duration | Reading | Rough price move per 1 point yield rise |
|---|---|---|
| Under 3: low | Short-dated or floating-rate-like behaviour | Under about 3% |
| 3 to under 7: moderate | Typical intermediate bond and fund territory | About 3% to 7% |
| 7 or more: high | Long maturities; rate moves dominate returns | About 7% or more |
Three reading rules. First, duration is a local measure: it is estimated at today’s price and yield level, and it drifts as both move, so recompute it after any large rate move rather than treating it as a permanent property of the bond. Second, for a portfolio, effective duration combines as the market-value weighted average of the holdings, which is why fund fact sheets report one portfolio figure. Third, a negative result from ordinary bond inputs is almost always an input error, most often P− and P+ entered in the wrong boxes; genuinely negative duration exists in instruments like interest-only mortgage strips, not in plain bonds.
What competing calculators miss
- Sign errors in the printed formula: at least one widely ranked effective duration tool prints the numerator as the price if yields increase minus the price if yields decrease, which flips the sign and returns a negative duration for a normal bond, and its own worked example then labels the higher price as the “yield increases” value to hide it. Here the numerator is P− minus P+, and the worked example above can be checked by hand in seconds.
- The percent trap: several tools ask for the yield change as a percentage and divide by 100 inside the formula, while others expect a decimal. Mixing the two conventions is a silent 100x error. This page takes the decimal only, says so on the field itself, and shows 0.01 in the loaded example.
- A wrong formula dressed up as effective duration: some explainer pages define effective duration as modified duration multiplied by (1 + yield ÷ periods). That product is Macaulay duration, not effective duration, and it contains no repricing and no option behaviour at all.
- No route to the shifted prices: most tools show four boxes and never explain that P− and P+ must come from a repricing that lets cash flows change. Enter fixed-cash-flow prices and you get modified duration with extra steps, which is precisely the mistake effective duration exists to avoid. The Financial Edge overview of bond duration draws the same fixed-versus-variable cash flow line.
Frequently asked questions
It is the approximate percentage change in a bond’s price for a one percentage point change in yields, estimated by repricing the bond at a lower and a higher yield and comparing the two prices. Because the repricing can let the bond’s cash flows change, it works for callable, putable, and mortgage-backed bonds, where simpler duration measures rest on cash flows that are not actually fixed.
No. There are no coupon, maturity, or call-schedule inputs, because the repricing is not done here. You supply the price if yields fall (P−) and the price if yields rise (P+) from your own pricing model, spreadsheet with an option model, or data vendor, and this tool applies the effective duration formula to those three prices and your shift size. Prices from a fixed-cash-flow calculation turn the result into modified duration, whatever the label says.
Enter the shift you used to reprice, written as a decimal: 0.01 for one percentage point (100 basis points), 0.005 for half a point, 0.0025 for 25 basis points. It must be the same shift on both sides. Entering 1 when you mean one point makes the duration 100 times too small, which is the most common error with this formula.
Modified duration is derived from Macaulay duration and assumes the bond’s cash flows never change, however far yields move. Effective duration is estimated from two repricings, so any change in expected cash flows, such as a call becoming likely when yields fall, is already inside the prices it uses. For an option-free bond the two numbers come out close; for a callable bond, effective duration is shorter, because the call limits the price gain.
Macaulay duration is a weighted average time: the average point at which you receive the bond’s cash flows, weighted by their present values. It answers a “when do I get my money back” question. Effective duration answers a “how much does the price move” question, using repriced values rather than the cash flow timetable. Both are expressed in years, which is why they are so often confused.
For an ordinary bond, a negative result almost always means P− and P+ were entered in the wrong boxes, so the lower price sits in the “yield decreases” field. Swap them and recalculate. True negative duration does exist in a few specialised instruments, such as interest-only mortgage strips, whose value can rise when yields rise, but it is not a property of plain bonds, callable or otherwise.
Use full (dirty) prices, including accrued interest, for all three inputs, on the same basis: all per 100 of par, or all as total currency amounts. Mixing a clean current price with full shifted prices distorts the price gap the formula divides, and mixing bases between inputs breaks it completely. Consistency across the three prices matters more than which consistent basis you choose.
Yes. A portfolio’s effective duration is the market-value weighted average of its holdings’ effective durations, which is the figure bond funds and ETFs report. Compute each holding with the same shift size, weight by market value, and add them up. Recompute after large rate moves, because each holding’s duration drifts as its price and yield level change.
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References
- XplainD. Bond Duration: Macaulay, Modified and Effective Duration. Accessed October 21, 2026.
- AnalystPrep. Effective Duration and Convexity for Option-Embedded Bonds (CFA Level I). Accessed October 21, 2026.
- AnalystPrep. Effective Duration: Measure of Interest Rate Risk (CFA Level I). Accessed October 21, 2026.
- Buetow, G. W. and Johnson, R. R. Handbook of Finance, Chapter 14: Effective Duration and Convexity. Accessed October 21, 2026.
- Financial Edge Training. Bond Duration: Modified vs Effective Duration. Accessed October 21, 2026.