Convert a nominal annual rate into EAR / APY, compare compounding frequencies, and audit the one-year effect.
Use the stated annual rate and compounding frequency. EAR and APY use the same pure compounding math here.
Pure rate conversion only. Fees, taxes, irregular cash flows and lender-specific APR rules are not included.
Enter a nominal annual rate and compounding frequency.
| Compounding | Periods/year | EAR / APY | Lift vs nominal |
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Uses the same compounding frequency selected above.
Assumes no deposits, withdrawals, fees or rate changes during the year.
For discrete compounding, r is the nominal annual rate as a decimal and n is compounding periods per year. Continuous compounding uses EAR = e^r − 1. Reverse mode algebraically solves the nominal rate that reproduces the selected EAR.
EAR, EIR, EAY and APY can describe the same one-year compounding conversion in this calculator. Product disclosures may use those labels differently. This page does not calculate regulatory APR, account fees, loan cash-flow IRR, promotional tiers, taxes or changing rates.
For fee-inclusive borrowing cost use the APR or loan-comparison tools. For multi-year savings balances and contributions use the savings or compound-interest tools.
Start with the broad calculator that matches the decision, then move to a specialist only when the loan structure, cash flow, tax treatment, debt strategy or savings goal genuinely changes.
connects debt payoff, credit-card cost, loan comparison, APR/APY, effective-rate, weighted-rate, and hypothetical consolidation calculations.
Results are deterministic browser-local math from the values you enter. They are useful for scenario comparison, but they are not a lender quote, approval decision, investment forecast, credit recommendation, or substitute for an account agreement.
A nominal annual rate states the annualized periodic rate before intra-year compounding. EAR or APY includes the compounding effect. Two products with the same nominal rate can have different effective rates if their compounding frequencies differ.
Solving from EAR/APY back to a nominal/stated annual rate finds the nominal rate that would produce the same one-year growth under the selected compounding frequency. It does not reconstruct fees, irregular cash flows or a lender-specific APR calculation.
For m compounding periods, the periodic rate is the nominal/stated annual rate divided by m and EAR is (1 + r/m)^m - 1. Continuous compounding uses an exponential relationship. Compare assumptions with the frequency table before copying a rate into another model.
Effective yield measures annual growth from compounding, but account fees, deposit timing, promotional tiers and taxes can change the realized return. Keep those terms separate from the pure rate conversion.
Take the nominal/stated annual rate, calculate EAR, then feed that EAR into the reverse solver at the same frequency. The recovered nominal rate should match within rounding. This round trip is a strong check for percentage-versus-decimal entry errors.
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