APR to APY Calculator

Convert between nominal APR and effective APY for a selected compounding frequency, or convert APY back to APR.

What are APR and APY?

Annual percentage rate (APR) is the nominal yearly rate before compounding effects. Annual percentage yield (APY) is the effective yearly rate after compounding at the selected frequency. The same nominal APR produces a higher APY when interest compounds more often.

Formula

APR to APY: APY (%) = ((1 + APR ÷ 100 ÷ n) ^ n − 1) × 100. APY to APR: APR (%) = n × ((1 + APY ÷ 100) ^ (1 ÷ n) − 1) × 100. Here n is compounding periods per year.

Worked example

A 12% APR compounded monthly has n = 12. The monthly factor is 1 + 0.12 ÷ 12 = 1.01. Raising 1.01 to the 12th power gives about 1.1268. Subtracting 1 and multiplying by 100 gives an APY of about 12.68%.

Assumptions and limitations

The Calculator uses a fixed nominal rate and a discrete compounding schedule. It does not include fees, tiered balances, promotional periods, or day-count conventions used by specific lenders or deposit products.

Common questions

Which rate should I compare for savings accounts?

APY reflects compounding and is usually better for comparing deposit products. Is APR the same as the interest rate on a loan advertisement? Loan APR often includes certain fees by regulation, but this Calculator models only the stated nominal rate and compounding frequency. Does compounding frequency matter? Yes. More frequent compounding increases APY for the same APR.

Methodology

The Calculator applies the standard effective-rate formulas with exact decimal arithmetic and rounds only the displayed converted rate.