Nominal Effective and Continuous Interest Rate Calculator
Compare equivalent annual interest-rate quotation conventions and compounding frequencies.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert the entered quotation to log annual growth. Derive effective annual, nominal-at-frequency and continuously compounded quotations from that same growth factor.
Effective=(1+nominal/f)^f−1; continuous=ln(1+effective); nominal=f×((1+effective)^(1/f)−1)
Worked example
6% nominal annual compounded monthly is about 6.16778119% effective annual and 5.98504981% continuously compounded annual.
Assumptions and input details
Quotation equivalence only, not a transaction quote or statutory APR calculation. Frequencies are whole 1–366; nominal period rate must exceed −100%. No fees, tax, cash-flow timing or day-count convention is included. Effective and nominal input rates support −99% to 1000%; continuous input supports −1000% to 1000%. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: OpenStax: stated versus effective rates · OpenStax: continuous compounding
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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