{
    "name": "Mean Absolute Error Calculator",
    "url": "https://calculators.geekmidst.com/calculators/mean-absolute-error-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/mean-absolute-error-calculator.md",
    "category": "Statistics & probability",
    "description": "Compute the mean absolute error between actual and predicted values, with the mean bias, median and maximum absolute error and RMSE for comparison.",
    "summary": "MAE is the average size of the prediction errors, ignoring their sign. It is in the same units as the data and every unit of error counts the same.",
    "also_called": [
        "MAE calculator",
        "Mean absolute deviation (forecast) calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "actual",
            "label": "Actual (observed) values",
            "type": "textarea",
            "default": "3, 5, 7, 9"
        },
        {
            "name": "predicted",
            "label": "Predicted (forecast) values, same order",
            "type": "textarea",
            "default": "2.5, 5.5, 7, 8"
        }
    ],
    "outputs": [
        {
            "key": "mae",
            "label": "MAE",
            "format": "number"
        },
        {
            "key": "bias",
            "label": "Mean error / bias (actual − predicted)",
            "format": "number"
        },
        {
            "key": "median_ae",
            "label": "Median absolute error",
            "format": "number"
        },
        {
            "key": "max_ae",
            "label": "Largest absolute error",
            "format": "number"
        },
        {
            "key": "rmse",
            "label": "RMSE, for comparison",
            "format": "number"
        },
        {
            "key": "n",
            "label": "Pairs (n)",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "eᵢ = actualᵢ − predictedᵢ;  MAE = Σ|eᵢ| ÷ n;  bias = Σeᵢ ÷ n",
        "variables": {
            "eᵢ": "error for pair i",
            "n": "number of pairs"
        }
    },
    "worked_example": {
        "inputs": {
            "actual": "3, 5, 7, 9",
            "predicted": "2.5, 5.5, 7, 8"
        },
        "steps": [
            "Errors: 0.5, −0.5, 0, 1; absolute errors 0.5, 0.5, 0, 1.",
            "MAE = 2 ÷ 4 = 0.5.",
            "Bias = (0.5 − 0.5 + 0 + 1) ÷ 4 = 0.25: on average the predictions are a little low."
        ],
        "result": "The predictions miss by 0.5 units on average and run 0.25 units low overall."
    },
    "interpretation": "MAE answers “how far off are we, typically?”. Pair it with the bias: a small bias with a large MAE means errors in both directions; a bias close to MAE means the model is consistently high or low and could be recalibrated.",
    "assumptions": [
        "Each predicted value is paired with the actual value in the same position.",
        "Errors are actual minus predicted, so a positive bias means under-prediction."
    ],
    "limitations": [
        "MAE is scale-dependent, so it cannot compare series measured in different units; use MAPE or a scaled error for that."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is MAE never larger than RMSE?",
            "answer": "Squaring before averaging gives large errors more weight, so RMSE ≥ MAE, with equality only when all errors are the same size."
        },
        {
            "question": "Which forecast minimises MAE?",
            "answer": "The median of the outcome distribution; the mean minimises RMSE."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "RMSE Calculator",
            "url": "https://calculators.geekmidst.com/calculators/root-mean-square-error-calculator"
        },
        {
            "name": "MAPE Calculator",
            "url": "https://calculators.geekmidst.com/calculators/mean-absolute-percentage-error-calculator"
        },
        {
            "name": "Percent Error Calculator",
            "url": "https://calculators.geekmidst.com/calculators/percent-error-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}