Enter your bond’s nominal value, current price, coupon rate, coupon frequency, settlement date and maturity date to calculate Yield to Maturity instantly. Six inputs, zero ambiguity, designed for fixed income professionals, finance students and individual bond investors.
Yield to Maturity (YTM) is the single most important metric in fixed income analysis. It answers the question: “What annualised total return will I earn if I buy this bond today and hold it to maturity?”
YTM is the discount rate that makes the present value of all future cash flows – coupon payments plus the principal repayment at maturity – exactly equal to the bond’s current dirty price. It captures both income (coupons) and capital gain or loss (the difference between purchase price and nominal value at maturity) in a single annualised figure.
This is fundamentally different from the coupon rate. The coupon rate is fixed and printed on the bond’s term sheet. YTM moves continuously with the bond’s market price. The two are equal only when the bond trades at exactly par (price = 100). At any other price, YTM and coupon rate diverge – and the difference is precisely what makes YTM the relevant metric for comparing bonds.
The face value the issuer repays at maturity. Standard nominals are $1,000 in the US, £100 in the UK, €1,000 in most of Europe. Nominal determines the dollar amount of each coupon payment and the principal cash flow at maturity.
The date the issuer repays the nominal value. Together with coupon frequency, this fully defines the bond’s remaining coupon schedule. The calculator works back from the maturity date in coupon-frequency intervals to reconstruct every remaining coupon payment date.
The date cash and securities change hands – typically T+1 for US Treasuries (since May 2024) and T+2 for corporate bonds in most markets. The calculator uses this date to determine accrued interest, derive the dirty price, and calculate the time to each future cash flow.
The bond’s market price as quoted on Bloomberg, broker screens or price feeds – excluding accrued interest. Enter as a percentage of nominal: 97.50 means the bond trades at 97.5% of face value.
The price drives the YTM directly. The calculator uses the price you enter to solve for the yield that reconciles all future cash flows with that price.
The annual interest rate the bond pays as a percentage of nominal value. A 4.5% coupon on $1,000 nominal pays $45 per year, distributed across coupon dates according to the frequency.
The coupon rate is fixed at issuance and does not change for a standard fixed-rate bond. The YTM the calculator produces will be different from the coupon rate whenever the bond trades at any price other than par.
How often the bond pays coupons per year:
Annual – one payment per year (some European corporates and sovereigns)
Semi-annual – two payments per year (US Treasuries, US corporate bonds, UK gilts, most international markets)
Quarterly – four payments per year (some structured products and FRNs)
Frequency affects the YTM calculation because compounding at different intervals produces different effective annual yields for the same nominal rate. A semi-annual bond compounding at half the YTM twice per year produces a slightly different effective annual yield than an annual bond compounding at the full YTM once per year.
YTM cannot be calculated with a single closed-form formula. Unlike Current Yield or the simple zero-coupon yield, YTM requires iterative numerical methods.
The fundamental equation:
Dirty Price = Σ [Coupon / (1 + r/n)^t] + Nominal / (1 + r/n)^N
Where:
r = annual YTM
n = coupon frequency (1, 2 or 4)
t = period number (1, 2, 3, …)
N = total remaining periods
Coupon = periodic coupon payment (nominal × coupon rate / n)
There is no algebraic way to rearrange this equation and solve for r directly. Instead, the calculator uses Newton-Raphson iteration:
This typically converges within 5-10 iterations. The result is the YTM accurate to the fourth decimal place – more than precise enough for practical use.
A corporate bond with the following characteristics:
| Input | Value |
|---|---|
| Nominal value | $1,000 |
| Maturity date | 15 March 2031 |
| Settlement date | 15 April 2026 |
| Current price (clean) | 95.50 |
| Coupon rate | 5.0% |
| Coupon frequency | Semi-annual |
Maturity 15 March 2031, semi-annual coupons → payments on 15 March and 15 September each year.
Last coupon before 15 April 2026: 15 March 2026 Next coupon: 15 September 2026
Total remaining cash flows from settlement:
10 coupons of $25 each ($1,000 × 5% / 2)
$1,000 principal at maturity
Days from 15 March to 15 April 2026: 31 days Days in current coupon period (15 March to 15 September): 184 days
Accrued Interest = $25 × (31 / 184) = $4.21
Dirty Price = 95.50 + (4.21 / 1000 × 100) = 95.921 Settlement Amount = $1,000 × 95.921 / 100 = $959.21
This is the figure that the YTM calculation must match.
The calculator tests different rates until it finds the one that makes the present value of all cash flows equal $959.21.
Trial 1 – YTM = 5.0% (semi-annual rate = 2.5%): Discounted cash flows total: $1,000 (matches par) Too high – bond is trading at discount, YTM must be > 5%
Trial 2 – YTM = 6.0% (semi-annual rate = 3.0%): Discounted cash flows total: $957.35 Slightly too low – YTM is just below 6.0%
Trial 3 – YTM = 5.97% (semi-annual rate = 2.985%): Discounted cash flows total: $959.21
YTM = 5.97% (annual, with semi-annual compounding)
The bond was purchased at $959.21 (a discount to its $1,000 nominal). Over the next 5 years, the investor receives:
10 coupon payments of $25 each = $250 total
$1,000 principal at maturity
Total cash received: $1,250 Capital gain: $1,000 – $959.21 = $40.79
The 5.97% YTM is the annualised return that captures both the $250 in coupon income and the $40.79 capital gain, accounting for the timing of each cash flow. This exceeds the 5% coupon rate because the discount price (95.50 < 100) provides additional capital appreciation that supplements the coupon income.
The relationship between bond price and YTM is the foundation of bond market analysis. Three scenarios:
| Clean Price | YTM vs Coupon Rate | Bond Status |
|---|---|---|
| Above 100 | YTM < Coupon Rate | Premium |
| Exactly 100 | YTM = Coupon Rate | Par |
| Below 100 | YTM > Coupon Rate | Discount |
A bond trading at 105 with a 5% coupon and 5 years to maturity might have a YTM of 3.9%. The high coupon income is partly offset by the capital loss at maturity (purchase price of 105 returning only 100). YTM captures both effects.
A bond trading at 90 with a 5% coupon and 5 years to maturity might have a YTM of 7.4%. The lower coupon income is more than compensated by the capital gain at maturity. YTM reflects this total return.
Two bonds with identical coupons and maturities can have very different YTMs if their market prices differ. Two bonds with identical YTMs can have very different coupon rates and prices. Comparing bonds by coupon rate alone is meaningless. YTM is the normalising metric that makes bonds directly comparable regardless of their original issue terms.
A 5% coupon, 5-year semi-annual bond at three different prices:
| Clean Price | Yield to Maturity |
|---|---|
| 90.00 | 7.31% |
| 95.00 | 6.13% |
| 100.00 | 5.00% |
| 105.00 | 3.91% |
| 110.00 | 2.86% |
A 20-point swing in price produces approximately a 4.5 percentage point swing in YTM. This price sensitivity is what duration measures – and why duration analysis is the natural next step after YTM calculation.
YTM equals the coupon rate only when a bond trades at exactly par (price = 100). At any other price, YTM differs from the coupon rate because it incorporates the capital gain or loss realised at maturity. A bond purchased at 95 returns 100 at maturity – that 5% capital gain is added to coupon income in the YTM calculation. A bond purchased at 105 loses 5% at maturity – that capital loss subtracts from coupon income in the YTM calculation.
No. YTM is the expected return assuming three specific conditions: the bond is held to maturity, every coupon is reinvested at the YTM rate, and the issuer makes all payments as scheduled. In practice, reinvestment rates typically differ from YTM (this is reinvestment risk), bonds are sometimes sold before maturity, and credit events can affect payments. YTM is a useful benchmark and the standard basis for bond comparison, but it is not a guaranteed outcome.
Both are required for accurate YTM. The settlement date determines accrued interest and the dirty price – the actual investment amount. The coupon frequency determines the compounding structure of the YTM calculation: a semi-annual bond’s YTM is calculated as the rate that, when divided by 2, discounts each semi-annual cash flow. Using the wrong frequency or settlement date produces approximate YTM rather than the precise rate.
Professional sources use the same iterative methodology. Small differences (typically 1-5 basis points) usually trace to day-count convention assumptions. US Treasuries use Actual/Actual day count; US corporate bonds typically use 30/360. If the quote source uses a different convention from this calculator, the YTMs will differ marginally. Always confirm the convention applicable to your specific bond when exact reconciliation is required.
Zero-coupon bonds have no periodic coupon payments and a much simpler yield calculation. The formula is direct: Yield = (Face Value / Purchase Price)^(1/Years) – 1. Use the dedicated Zero-Coupon Bond Yield Calculator for zero-coupon analysis. While this calculator can be configured with a 0% coupon rate, the simpler closed-form formula in the dedicated calculator is more efficient.
Newton-Raphson iteration with convergence tolerance below 0.0001 produces YTM accurate to the fourth decimal place – typically within 0.01% of the true value. Differences from other sources almost always trace to input assumptions (day-count, settlement date, accrued interest treatment) rather than the calculation itself.
Yes, continuously. YTM reflects the relationship between the current price and all remaining cash flows. As time passes, remaining cash flows decrease, the bond approaches maturity, and the price-yield relationship adjusts. Even with a stable market price, YTM drifts as time passes. Portfolio yield calculations require regular recalculation rather than relying on yields recorded at purchase.
Yield to call (YTC) is the YTM calculated assuming the bond is called by the issuer at the next call date, rather than held to maturity. For callable bonds trading above the call price, sophisticated analysts calculate both YTM and YTC and use the lower of the two as the relevant yield (because the issuer will call if it benefits them, meaning the lower yield is the realistic outcome). This calculator computes YTM assuming hold-to-maturity. For callable bonds, also use the Effective Duration Calculator to capture call option effects on duration.
YTM is the starting point for most bond analysis. The output of this calculator feeds directly into other tools on the site:
For the full theory of bond pricing, coupon structures and yield dynamics:
👉 Coupon Bonds Explained: How They Work, Pricing & Yield
For the broader context of bond markets and fixed income fundamentals:
Bond Accrued Interest & Dirty Price Calculator – calculate accrued interest and dirty price as standalone values for any bond
Bond Duration Calculator – Macaulay Duration and Modified Duration for any bond
Effective Duration Calculator – interest rate sensitivity for option-embedded bonds
Zero-Coupon Bond Yield Calculator – yield for bonds without periodic coupons
Repo & Reverse Repo Calculator – repo financing calculations using dirty prices