Bond Yield Calculator
Compute yield to maturity (YTM), current yield, and key risk metrics for any fixed-rate bond. Or reverse it — find the bond price from a target yield.
Rows = Yield shift (bps), Columns = Metric
| Yield Shift | New Yield | Est. Price (Duration) | Est. Price (Dur+Conv) | Actual Price | Price Change |
|---|
| Period | Date (Approx) | Coupon | Principal | Total CF | Discount Factor | PV of CF |
|---|
How to Use This Bond Yield Calculator
Start with the bond’s basics: face value (almost always $1,000 for US corporate and government bonds), coupon rate (the annual interest rate printed on the bond), and years to maturity. Most US bonds pay coupons semi-annually, but you can switch to annual or quarterly.
In “Yield from Price” mode, enter the bond’s current market price to compute the yield to maturity — the annualized return you’d earn if you held to maturity and reinvested all coupons at the same rate. In “Price from Yield” mode, enter a target YTM and the calculator will give you the fair price.
The results include duration and convexity — the two key measures of how sensitive the bond’s price is to changes in interest rates. Use the sensitivity tab to see exactly how much the price moves for different yield shifts.
Bond Yield Formulas
Current yield is the quick-and-dirty measure — it tells you the income return based on the price you pay, but ignores the capital gain or loss at maturity. YTM is the complete picture: it accounts for coupon payments, the time value of each payment, and the difference between your purchase price and the face value returned at maturity.
This calculator uses Newton’s method to iteratively solve for YTM — the same approach used by Bloomberg terminals and institutional bond analytics. The result is precise to within 0.0001%.
Premium, Discount, and Par Bonds
A bond’s price relative to its face value tells you how its coupon rate compares to current market yields. This relationship is the single most important concept in fixed-income investing.
| Bond Price | Relationship | YTM vs Coupon | What It Means |
|---|---|---|---|
| Below par ($950 on $1,000) | Discount | YTM > Coupon Rate | Market demands a higher yield than the coupon provides — you get a capital gain at maturity |
| At par ($1,000) | Par | YTM = Coupon Rate | Coupon rate exactly meets market requirements |
| Above par ($1,050 on $1,000) | Premium | YTM < Coupon Rate | Coupon exceeds market requirements — you take a capital loss at maturity, offset by higher income |
When the Federal Reserve raises rates, existing bonds with lower coupons become less attractive, so their prices fall (they trade at a discount). When rates drop, existing bonds with higher coupons become more valuable, so their prices rise (premium). This inverse relationship between interest rates and bond prices is the fundamental law of fixed income.
Duration: Your Interest Rate Risk Ruler
Duration measures how sensitive a bond’s price is to changes in yield. A bond with a duration of 7 years will lose approximately 7% in price if yields rise by 1 percentage point (100 basis points). It works in reverse too — a 1% decline in yields produces roughly a 7% price increase.
| Metric | What It Measures | How to Use It |
|---|---|---|
| Macaulay Duration | Weighted-average time to receive cash flows (in years) | Immunization, liability matching |
| Modified Duration | % price change per 1% yield change | Quick price sensitivity estimate |
| Convexity | Curvature of the price-yield relationship | Refines duration estimate for large yield moves |
For small yield changes (±25 bps), modified duration alone is accurate enough. For larger moves (±100+ bps), you need the convexity adjustment — duration overestimates losses and underestimates gains because the price-yield curve is convex, not a straight line. The sensitivity table on this calculator shows both estimates side by side.
Longer maturity = higher duration. Lower coupon = higher duration. Lower yield = higher duration. A zero-coupon bond has the highest duration of any bond with the same maturity (its duration equals its maturity). These three levers — maturity, coupon, and yield — are what you adjust to manage interest rate risk in a fixed-income portfolio.
Yield to Maturity vs Current Yield vs Coupon Rate
These three numbers are often confused but measure fundamentally different things. Coupon rate is fixed at issuance and never changes. Current yield and YTM change every time the bond’s market price moves.
| Measure | Formula | Includes Cap Gain/Loss? | Includes Time Value? | Best For |
|---|---|---|---|---|
| Coupon Rate | Annual coupon ÷ face value | No | No | Understanding the bond’s contractual payments |
| Current Yield | Annual coupon ÷ market price | No | No | Quick income comparison at current price |
| Yield to Maturity | IRR of all future cash flows | Yes | Yes | True total return comparison across bonds |
YTM’s biggest limitation is the reinvestment assumption: it assumes you can reinvest every coupon payment at the YTM rate for the remaining life of the bond. In a falling-rate environment, this overstates your actual realized return. In a rising-rate environment, it understates it. For this reason, YTM is best used as a comparison metric between bonds, not a guaranteed return prediction.
How Interest Rate Changes Affect Bond Prices
The price-yield curve on this calculator visualizes the inverse relationship — as yields rise, prices fall, and the curve flattens. The curvature is convexity, and it’s your friend as a bondholder: prices rise more than duration predicts when yields fall, and fall less than predicted when yields rise.
| If Yields Move… | Bond Price (Duration 5) | Bond Price (Duration 10) | Bond Price (Duration 20) |
|---|---|---|---|
| −200 bps | +10.0% (approx) | +20.0% | +40.0% |
| −100 bps | +5.0% | +10.0% | +20.0% |
| +100 bps | −5.0% | −10.0% | −20.0% |
| +200 bps | −10.0% | −20.0% | −40.0% |
These are linear approximations (duration only). With convexity, actual price gains from falling rates are slightly larger, and actual losses from rising rates slightly smaller. That asymmetry is what makes convexity valuable — and why investors sometimes pay a premium for high-convexity bonds.
Related Tools
| Calculator | Use It For |
|---|---|
| Present Value Calculator | Discount any future cash flow at a given rate |
| Future Value Calculator | Project a lump sum forward at a given yield |
| Compound Interest Calculator | General compounding — savings, reinvestment |
| WACC Calculator | Compute cost of capital using the risk-free rate from bonds |
| DCF Calculator | Discount equity cash flows using a rate informed by bond yields |
| Inflation Calculator | Adjust nominal bond yields for purchasing power |
FAQ
What is yield to maturity (YTM)?
YTM is the total annualized return you’d earn if you bought a bond at its current market price, held it until maturity, and reinvested all coupon payments at the same YTM rate. It accounts for coupon income, the time value of money, and any capital gain or loss between your purchase price and the face value repaid at maturity. It’s the standard metric for comparing bonds with different coupons, prices, and maturities.
What’s the difference between current yield and YTM?
Current yield is simply the annual coupon divided by the current price — it tells you the income yield but ignores capital gains/losses and the time value of money. YTM is the full-picture metric: it factors in both the coupon stream and the price convergence toward par at maturity. For a discount bond, YTM is higher than current yield (you get income plus capital appreciation). For a premium bond, YTM is lower.
Why do bond prices fall when interest rates rise?
Because new bonds issued at higher rates are more attractive than existing bonds with lower coupons. For the existing bond to compete, its price must drop until its yield matches the new market rate. This is the fundamental inverse relationship between interest rates and bond prices — it’s mechanical, not a matter of opinion.
What is duration and why does it matter?
Duration measures how sensitive a bond’s price is to yield changes. Modified duration tells you the approximate percentage price change for a 1% move in yields. A duration of 7 means roughly a 7% price drop for every 1% yield increase. Longer-maturity, lower-coupon bonds have higher duration — they’re more exposed to rate moves. Duration is the primary tool for managing interest rate risk in bond portfolios.
What is convexity?
Convexity measures the curvature of the price-yield relationship. Duration gives a linear approximation, but the actual relationship is curved. Convexity captures that curvature: it makes price gains from falling yields slightly larger, and price losses from rising yields slightly smaller, than duration alone predicts. High convexity is desirable — it means more upside and less downside for the same yield move.
What does it mean when a bond trades at a premium?
A premium bond has a market price above its face value (above $1,000 for most bonds). This happens when the bond’s coupon rate exceeds current market yields — investors are willing to pay more for the higher income stream. The premium gradually amortizes to par as the bond approaches maturity, so the YTM will be lower than the coupon rate.
How does coupon frequency affect yield?
More frequent coupon payments mean you receive cash sooner, which increases the bond’s yield slightly (because of compounding). A semi-annual bond with a 5% coupon actually yields slightly more than 5% on an effective annual basis, because you can reinvest the first coupon halfway through the year. The difference is small — usually 5–15 basis points — but it matters for precise comparison.
Can I use this calculator for Treasury bonds?
Yes. US Treasury bonds, notes, and many corporate bonds pay semi-annual coupons with a $1,000 face value — those are the defaults on this calculator. Treasury prices are often quoted as a percentage of face value (e.g., “99.50” means $995), so if your quote is in percentage terms, multiply by 10 to convert to dollars for a $1,000 face value bond.
Key Takeaways
- YTM is the standard bond comparison metric — it accounts for coupon income, capital gain/loss, and time value. Current yield and coupon rate do not.
- Bond prices and yields move inversely — when rates rise, existing bond prices fall. When rates fall, prices rise. Duration quantifies exactly how much.
- Duration is your interest rate risk measure — a modified duration of 7 means ~7% price change per 1% yield move. Longer maturity and lower coupons increase duration.
- Convexity is your friend — it means you gain more than expected when yields fall and lose less than expected when yields rise. High convexity is desirable.
- Premium bonds aren’t “expensive” — they have higher coupons and lower YTM. Discount bonds aren’t “cheap” — they have lower coupons and higher YTM. Price relative to par tells you coupon vs market rate, not value.
- YTM assumes reinvestment at the same rate — in reality, you may earn more or less on reinvested coupons. Use YTM for comparison, not as a guaranteed return.