Calculators

Root Mean Squared Logarithmic Error Calculator

Calculate RMSLE from non-negative actual and predicted pairs privately in your browser.

Measure root mean squared logarithmic error from paired non-negative actual and predicted values. Your data stays in your browser.

Enter one pair per line: actual, predicted. Separate the two values with a comma, semicolon, or space. Zero actuals and predictions are supported. Negative values are rejected. Nonzero magnitudes must be between 1e-100 and 1e100. Up to 10000 pairs; scientific notation supported; omit thousands separators. Use consistent units.

Your prediction error results will appear here.

Compare predictions on a logarithmic scale.

RMSLE = sqrt(Σ[ln(1 + predicted) − ln(1 + actual)]² / n). Natural logarithms and the +1 offset support zeros. For actual 0 and predicted 1, RMSLE is ln(2), approximately 0.69314718056. Zero means every prediction matches; lower is better. The result is not a percentage or an accuracy score. Logarithms reduce the influence of large absolute errors compared with RMSE. For a fixed actual value, equal absolute underprediction and overprediction need not have equal penalties. Input units and rescaling affect the result because of the +1 offset; compare models on the same observations and scale. Negative values are unsupported. Enter up to 10000 pairs, one per line, separated by a comma, semicolon, or spaces. Nonzero values must be between 1e-100 and 1e100. Scientific notation is accepted; omit thousands separators. Log1p, scaled squares, and compensated summation reduce numerical error; browser floating-point rounding can still hide very small differences. Results show up to 12 significant digits. All data stays in your browser.

Frequently Asked Questions

Everything you need to know about this tool, how it works, and privacy.

How is RMSLE calculated?

Take the natural logarithm of 1 plus each actual and prediction, square their difference, average those squares, and take the square root. For actual 0 and predicted 1, the result is ln(2), approximately 0.69314718056.

Can I use zeros or negative numbers?

Zeros are valid because ln(1 + 0) is zero. This calculator rejects negative actuals and predictions; it does not clip or shift them.

Is RMSLE a percentage?

No. RMSLE measures error in logarithmic space. Zero indicates an exact match on every pair; there is no universal good threshold.

How does RMSLE differ from RMSE?

RMSE measures errors in the original units and emphasizes large absolute errors. RMSLE compares logarithms after adding 1. Changing input units affects RMSLE, so use the same scale and observations for comparisons.