AtlasCalcsUtility Calculation Suite
2026-09-22 7 min read

Modified Duration Calculator

Modified duration and the price move per 1% yield change for a bond. Live calculator with worked steps, charts and formulas.

Calculator

Face (Par) Value Help
$

Principal repaid at maturity, usually $1,000.

Annual Coupon Rate(%) Help
%

Interest paid on face value each year.

Yield to Maturity(%) Help
%

Market discount rate used to price the bond.

Years to Maturity(years)
years
Coupon Frequency
Yield Shock for Sensitivity(%)
%

This bond calculators calculator runs on standard bond mathematics: coupons and face value discounted at the market yield with 2 payment(s) per year. Money is calculated at full precision and rounded only for display.

Results

Optimal

Macaulay Duration

7.89 yrs

Weighted-average time to receive cash flows.

Modified Duration (Headline)

7.67 yrs

Price sensitivity per 1% yield move.

Price Move per 1% Yield Rise

7.67%

Approximate % fall in price.

Maturity

10.0 yrs

Live results update as you type — currently showing macaulay duration of 7.89 yrs. Replace the defaults with your own quote for an exact comparison.

Visualizations

Interest-Rate Risk (Modified Duration)

7.7yrs
020

Formula

The tradable risk number: percent price change per one-point yield change.

ModD = MacD ÷ (1+y/m)

Variables

SymbolNameUnitDescription
ModDModified durationyearsRisk measure

Explanation

Percent price move for a one-percentage-point yield move.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Weight each cash flow by its arrival time.

MacD = Σ t·PV(CF) ÷ Price
Result: 7.89 years
Step 2

Adjust for compounding frequency to get price sensitivity.

ModD = MacD ÷ (1 + y/m)
Result: 7.67 years
Step 3

Read sensitivity directly: a 1% yield rise cuts price ~ModD%.

ΔP/P ≈ −ModD × Δy
Result: −7.67% per +1% yield
Final Answer
7.89 yrs

Worked Examples

See how the calculator works with different scenarios.

Scenario

The modified duration calculator run on the values above, showing the full calculation path rather than only the answer.

Inputs

Face (Par) Value:1000
Annual Coupon Rate:5
Yield to Maturity:6
Years to Maturity:10

Calculation

1. Weight each cash flow by its arrival time. → 7.89 years 2. Adjust for compounding frequency to get price sensitivity. → 7.67 years 3. Read sensitivity directly: a 1% yield rise cuts price ~ModD%. → −7.67% per +1% yield

Result

Macaulay Duration: 7.89 yrs

Interpretation

MacD 7.89y, ModD 7.67y — a 1% yield rise moves price ≈ 7.67%.

Understanding Your Result

Your Result: Macaulay Duration: 7.89 yrs

What This Means

Percent price move for a one-percentage-point yield move.

Why It Matters

MacD 7.89y, ModD 7.67y — a 1% yield rise moves price ≈ 7.67%.

Professional Interpretation

MacD 7.89y, ModD 7.67y — a 1% yield rise moves price ≈ 7.67%.

How this is calculated

The tradable risk number: percent price change per one-point yield change.

What drives the result

Each cash flow arrives at a different time, so the bond responds like a weighted average of zeros. Longer maturities, lower coupons and lower yields all extend duration and raise volatility. Convexity is always positive for plain bonds, which cushions falls and amplifies rises.

Recommendations

  • •Match duration to your horizon to immunize rate risk.
  • •Longer duration = larger price swings both ways.

Educational Content

Introduction

Duration and convexity translate yield moves into price moves. Duration gives the linear estimate (a 1% yield rise cuts price by roughly the modified duration in percent); convexity corrects for curvature on large moves and long maturities.

Concept Explanation

Each cash flow arrives at a different time, so the bond responds like a weighted average of zeros. Longer maturities, lower coupons and lower yields all extend duration and raise volatility. Convexity is always positive for plain bonds, which cushions falls and amplifies rises.

Applications

▸Sizing interest-rate risk before a central-bank decision
▸Matching asset duration to a spending horizon (immunization)
▸Comparing a long zero with a short high-coupon bond on volatility
▸Estimating price impact of a 1–2% yield shock

Benefits

  • •Turns abstract rate risk into a percent price move
  • •Shows which bond in a pair swings more for the same shock
  • •Separates linear (duration) from curvature (convexity) effects
  • •Works for any plain-vanilla coupon bond

Limitations

  • •Linear estimates break down for large yield shocks without convexity
  • •Callable bonds exhibit negative convexity near the call price
  • •Assumes a parallel shift of the whole curve
  • •Credit-spread moves are not separated from rate moves

Best Practices

  • •Match duration to your horizon rather than maximizing yield
  • •Add convexity for shocks above 1% or maturities above 10 years
  • •Prefer higher convexity when yields are equally uncertain both ways
  • •Recheck duration after big rate moves — it drifts with yield

Common Misconceptions

Myth: Duration is the same as maturity
Truth: Duration is a weighted-average time in years; only zeros have duration equal to maturity.
Myth: High yield always means high risk
Truth: Yield compensates several risks (rate, credit, liquidity). Duration isolates the rate piece.

Practical Tips

  • •Scale linearly for small moves; add convexity past 1%.

Common Mistakes

Applying duration to huge shocks
Add convexity — duration alone understates long-bond moves.

Assumptions

This calculator makes the following assumptions to provide estimates:

Yield compounding matches frequency: Standard street convention.

Limitations

Be aware of these limitations when using this calculator:

Limitation: Linear estimates break down for large yield shocks without convexity
Limitation: Callable bonds exhibit negative convexity near the call price
Limitation: Assumes a parallel shift of the whole curve
Limitation: Credit-spread moves are not separated from rate moves

Frequently Asked Questions

Answers to common questions about this calculator.

Why do traders quote modified, not Macaulay?
It reads directly as risk: ModD 7 ≈ −7% per +1% yield.
Who uses the modified duration calculator?
It is used by investors comparing bond options, by advisers checking a quote before a client commits, and by planners sizing contributions for a goal. It sits in the Bond Calculators group of the Bonds & Fixed Income section of Atlascalcs.
How accurate is the modified duration calculator?
Every figure follows directly from the inputs using standard bond mathematics, so it is accurate to the quality of the values you enter. Dealer quotes round to cents and apply day-count conventions, so expect pennies of difference on accrued interest and settlement figures.
How current are the yields used here?
The calculator uses the figures you enter, so update the yield to your dealer quote or auction result. Market yields move intraday; ratio and tax thresholds follow the conventions in the references.
Does rounding change the results?
All math runs at full precision and rounds only for display. Dealers round to cents and apply day-count conventions, so expect pennies of difference on accrued interest.
Should I compare coupons or yields?
Always yields (YTM for total return, current yield for income). Two bonds with different coupons price identically at the same YTM.
What should I have ready before buying?
Face, coupon, maturity, frequency, price or yield, settlement date, tax bracket and any call or conversion terms. With those, every figure here ties to a quote.

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Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Duration
Weighted-average time to cash flows (Macaulay) and price sensitivity (modified).

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

Present-value pricing with periodic compounding at the quoted yieldYTM solved numerically (bisection) to full precision; display rounded onlyT-Bill bank discount on 360 days; investment yield on 365 daysMoney rounded for display only; all calculations run at full precision

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Page Information

Last Updated:

2026-09-22

Version:

2.0.0

License:

Free to use for educational and professional purposes.