Bond Duration (Macaulay) Calculator

Compute Macaulay duration price and risk for coupon and zero coupon bonds with flexible frequency settings interactive schedules clear formulas a price yield curve and convexity for better accuracy export results to CSV or PDF with an elegant white interface built for analysts students and investors seeking fast insights reliable numbers and practical decisions

Inputs
$
Key Results
Clean Price (per Face)
Macaulay Duration (years)
Modified Duration (years)
Convexity (years²)
DV01 (per 100 Face)

PV weight distribution across cash flows.
Price–Yield Curve

Curve shows price versus yield around the entered YTM holding coupon schedule constant. Useful to visualize rate sensitivity and convexity.

Example Data Table

Click “Use” to load a preset into the input panel.

FaceCoupon %YTM %YearsFreq
10005652
100032.5102
10000431
Formula Used

Let F be face value, c the annual coupon rate, y the annual yield to maturity, m payments per year, and N = m × years the number of coupon periods. The per‑period coupon is C = F × c / m. The present value (price) is

P = Σ (t=1..N) [ CFₜ / (1 + y/m)ᵗ ],
where CFₜ = C for t < N, and CF_N = C + F.

The Macaulay Duration (in years) is

D_Mac = (1/P) × Σ (t=1..N) [ (t/m) × CFₜ / (1 + y/m)ᵗ ]

The Modified Duration is

D_Mod = D_Mac / (1 + y/m)

The Modified Convexity (in years²) with discrete compounding is

C_Mod = (1/P) × Σ (t=1..N) [ CFₜ × t × (t + 1) / (1 + y/m)^(t+2) ] / m²

Small price change approximation for a yield shift Δy (in decimal):

ΔP / P ≈ - D_Mod × Δy + 0.5 × C_Mod × (Δy)²
How to Use
  1. Enter face value, coupon rate, yield to maturity, years, and pick payments per year.
  2. Press Calculate to compute price, Macaulay duration, modified duration, convexity, and DV01.
  3. Review the cash flow schedule and the PV weight chart to see timing of value.
  4. Use the price–yield curve to visualize sensitivity and curvature around the current yield.
  5. Export the schedule as CSV or PDF for audit, sharing, or further analysis.

Notes: Compounding assumes nominal APR with m compounding periods. Clean price equals PV of future cash flows from next coupon date (no accrued interest modeling).

FAQs

It is the present value weighted average time to receive a bond’s cash flows measured in years. Higher duration implies higher sensitivity of price to yield changes.

Modified duration equals Macaulay duration divided by (1 + y/m). It approximates the percentage price change for a 1% change in yield under the given compounding convention.

Yes. Set coupon rate to 0. The schedule will show a single redemption cash flow and duration will equal time to maturity (subject to frequency rounding).

Changing payments per year alters discounting and the schedule. More frequent coupons generally shorten Macaulay duration because cash flows arrive earlier.

Convexity improves the duration based estimate for larger rate moves. Higher convexity means the price falls less when yields rise and rises more when yields fall.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.