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Bond Duration (Macaulay)

Quick answer

Macaulay duration weights each cash flow by its time: a 5-year 6% annual bond at par has duration ≈4.46 years — the effective payback.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the Bond Duration Calculator Work?

Duration = Σ (t × PV(CFₜ)) ÷ price

Macaulay duration is the weighted-average time to receive a bond's cash flows, with weights of present value. Longer duration means more rate sensitivity. The calculation follows Duration = Σ (t × PV(CFₜ)) ÷ price. A 5-year 6% annual-coupon bond priced at par pays 6, 6, 6, 6 and 106; weighting each by present value gives a duration of ≈4.46 years — cash arrives, on average, in 4.46 years. The result updates instantly whenever you change an input, and every figure is shown in the same currency or units you entered, with no hidden conversion applied.

  1. 1

    Step 1

    Enter the required figures for the Bond Duration Calculator in the fields above.

  2. 2

    Step 2

    The tool applies Duration = Σ (t × PV(CFₜ)) ÷ price to your numbers automatically.

  3. 3

    Step 3

    Read the result, shown in the same units you entered.

  4. 4

    Step 4

    Adjust the inputs to compare scenarios side by side.

Use Cases

Rate-risk comparison

Ranking bonds before a rate view

Immunization

Matching portfolio duration to a liability date

Fund screening

Comparing duration across bond ETFs

Pension liability matching

Aligning asset timing with payouts

Common Mistakes

  • Equating duration with maturity

  • Ignoring yield dependence

  • Forgetting frequency

FAQs

Why does a longer coupon bond have shorter duration than maturity?

Coupons return money early: the 5-year 6% bond averages 4.46 years because you hold cash before maturity; only zeros have duration equal to maturity.

How does duration connect to price risk?

Multiply by (1+y): a 4.46 duration at 8% yield means ≈4.13% price drop per 1% rate rise — modified duration is that link.

What formula does the Bond Duration Calculator use?

It computes Duration = Σ (t × PV(CFₜ)) ÷ price — with t is each payment's year and PV its present value.

Which input moves the result most?

In most Bond Duration Calculator runs the rate and the time horizon swing the answer hardest — test those first.

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