The formula
How to calculate bond duration
Duration measures how sensitive a bond's price is to a change in interest rates. Macaulay duration is the weighted average time until you get your money back; modified duration converts that into a percentage price move per 1% shift in yields.
The closed form above avoids discounting each coupon separately. It assumes annual coupons and a flat yield curve, which is the standard textbook setup and close enough for comparing bonds.
Fill in the following:
- Coupon rate (%)
- Yield to maturity (%)
- Years to maturity (years)
Results appear immediately — there is nothing to submit. Changing a field rewrites the link, so you can share the exact scenario you are looking at.
The order the fields are filled in makes no difference to the result — the calculator recomputes the whole formula from whatever is currently in every field, not step by step. That means it is safe to adjust one number, watch the result change, and adjust it back, without worrying about resetting anything first.
Why bond duration matters
A calculation like this usually gets used at a decision point rather than out of curiosity — comparing two real options, checking a number a lender or adviser has quoted, or working out whether a plan that sounded fine in conversation still holds up once it is written down with actual figures. The maths itself is rarely complicated; what is hard is remembering which figures to use and in what order, which is exactly what a dedicated calculator is for.
Beyond a one-off check, the same calculation is worth revisiting whenever the underlying numbers change — a new interest rate, a change in income, a different term. Because the figures live in the page's own web address, coming back to update just one field and compare the new result against the old one takes seconds rather than starting again from a blank page.
The reason a page like this exists at all, rather than leaving the calculation to a spreadsheet or a textbook appendix, is that the formula behind bond duration is fiddly enough to get wrong by hand but not complicated enough to need specialist software. That middle ground — real enough maths to matter, simple enough to check instantly — is exactly what a dedicated calculator is for, and it is why the same figure recalculated here should match a careful manual calculation almost exactly.
A calculator like this one is often bookmarked and returned to repeatedly over months rather than used once, particularly for anything tied to an ongoing plan such as a mortgage, a savings goal or an investment being tracked. Because the figures live in the web address rather than only in memory, coming back to the same page with updated numbers is quicker than starting from a blank spreadsheet each time.
Worked example
Take the figures the calculator starts with:
- Coupon rate: 4.5 %
- Yield to maturity: 6 %
- Years to maturity: 10 years
That gives:
- Macaulay duration: 8.147 years
- Modified duration: 7.686 years
- Price change if yields rise 1%: -7.686 %
These figures are only the calculator's own starting values, included so the working is visible rather than hidden inside the tool above. Replace them with your own numbers and the same arithmetic applies — nothing about the method changes, only the inputs feeding it.
Reading the result
Modified duration is a rule of thumb you can apply directly: 7.5 means a one-point rise in yields costs roughly 7.5% of the price. A zero-coupon bond has duration equal to its maturity; coupons shorten it, because some of your money comes back sooner.
Where this goes wrong. Duration is a straight-line estimate of a curved relationship. For yield moves beyond about one percentage point it overstates losses and understates gains — the correction term is convexity.
A useful check on any unfamiliar result is to compare it against a rough mental estimate first — round the inputs to convenient numbers and see whether the calculator's answer lands in roughly the same territory. A wildly different figure usually means one of the fields was entered in the wrong unit, most often a percentage typed as a whole number where a decimal was expected, or the reverse.
Because Macaulay duration genuinely is a time: the average number of years until each pound of the bond's cash flows arrives, weighted by present value. Modified duration inherits the unit even though it is used as a sensitivity.
Hold shorter-dated bonds, prefer higher coupons, or ladder maturities so that some of the portfolio is always redeeming and can be reinvested at current rates.
It returns macaulay duration. With 4.5 % coupon rate, 6 % yield to maturity and 10 years years to maturity, that comes to 8.147 years. Change any field and the figure moves with it.
Whenever one of the underlying figures changes — a new interest rate, a different balance, an updated term — since the result only reflects what is currently in the fields. There is no need to keep a separate record of past results; the web address for a filled-in version already carries the figures used to produce it.
Not unless a tax rate or a fee is explicitly one of the inputs above. Where it is not, the figure shown is a gross calculation, and any tax due depends on your personal circumstances and current tax rules, which are worth checking separately.
The arithmetic itself is exact — the calculator applies the formula shown above precisely, with no rounding until the final figure is displayed. The uncertainty, where it exists, is entirely in the inputs: an estimated rate or an approximate balance carries that same approximation through to the result.