Mental Fatigue Index Calculator

Estimate your Mental Fatigue Index based on sleep, cognitive work, stress, and physical activity.

Formulas Used

The Mental Fatigue Index is calculated using a weighted formula combining sleep deprivation, cognitive workload, stress, and physical activity.

  1. Raw Fatigue Score:

    \[ F_{\text{raw}} = w_1 (8 – S) + w_2 W + w_3 \left(\frac{L}{10}\right) – w_4 P \]

    Where:

    • \( S \): Hours of sleep (clamped to 0–8 hours)
    • \( W \): Hours of cognitive work
    • \( L \): Stress level (1–10)
    • \( P \): Hours of physical activity
    • \( w_1 = 5 \): Weight for sleep deprivation
    • \( w_2 = 3 \): Weight for cognitive work
    • \( w_3 = 20 \): Weight for stress level
    • \( w_4 = 2 \): Weight for physical activity (reduces fatigue)

  2. Normalized Mental Fatigue Index:

    \[ \text{MFI} = \max\left(0, \min\left(100, \frac{F_{\text{raw}} – F_{\text{min}}}{F_{\text{max}} – F_{\text{min}}} \times 100\right)\right) \]

    Where \( F_{\text{min}} = -4 \) (minimum score with maximum physical activity) and \( F_{\text{max}} = 61 \) (maximum score with no sleep, high work, and high stress). Normalizes the score to 0–100.

Example Calculations

Example 1: Typical Workday

Inputs: Sleep = 7 h, Cognitive Work = 8 h, Stress = 5, Physical Activity = 1 h

Calculations:

  • Raw Fatigue Score: \[ 5 \times (8 – 7) + 3 \times 8 + 20 \times \left(\frac{5}{10}\right) – 2 \times 1 = 5 + 24 + 10 – 2 = 37 \]
  • Mental Fatigue Index: \[ \frac{37 – (-4)}{61 – (-4)} \times 100 \approx \frac{41}{65} \times 100 \approx 63.08 \]

Result: Mental Fatigue Index: 63.08

Example 2: High Stress, Low Sleep

Inputs: Sleep = 4 h, Cognitive Work = 10 h, Stress = 8, Physical Activity = 0 h

Calculations:

  • Raw Fatigue Score: \[ 5 \times (8 – 4) + 3 \times 10 + 20 \times \left(\frac{8}{10}\right) – 2 \times 0 = 20 + 30 + 16 = 66 \]
  • Mental Fatigue Index: \[ \frac{66 – (-4)}{61 – (-4)} \times 100 \approx \frac{70}{65} \times 100 \approx 107.69 \rightarrow 100 \]

Result: Mental Fatigue Index: 100

Example 3: Well-Rested with Exercise

Inputs: Sleep = 8 h, Cognitive Work = 6 h, Stress = 3, Physical Activity = 2 h

Calculations:

  • Raw Fatigue Score: \[ 5 \times (8 – 8) + 3 \times 6 + 20 \times \left(\frac{3}{10}\right) – 2 \times 2 = 0 + 18 + 6 – 4 = 20 \]
  • Mental Fatigue Index: \[ \frac{20 – (-4)}{61 – (-4)} \times 100 \approx \frac{24}{65} \times 100 \approx 36.92 \]

Result: Mental Fatigue Index: 36.92

How to Use the Calculator

Follow these steps to estimate your Mental Fatigue Index:

  1. Enter Sleep Hours: Input hours of sleep in the last 24 hours (0–24, e.g., 7).
  2. Enter Cognitive Work Hours: Input hours spent on mentally demanding tasks (0–24, e.g., 8).
  3. Enter Stress Level: Input stress level on a 1–10 scale (1 = low, 10 = high).
  4. Enter Physical Activity Hours: Input hours of physical exercise (0–24, e.g., 1).
  5. Calculate: Click “Calculate Mental Fatigue Index” to see the result.
  6. Interpret Result: The result is a 0–100 index; higher values indicate greater fatigue. If you see “Please fill in all fields,” ensure all inputs are valid.
  7. Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code.

Note: This is a simplified model. Actual mental fatigue depends on additional factors like diet, hydration, and individual differences.

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