Learning Retention Rate Calculator

Learning Retention Rate Calculator estimates retention, decay, and efficiency based on study time, review, and method.

Study Time (hours):

Review Frequency:

Material Complexity:

Learning Method:

Formulas Used in Learning Retention Rate Calculator

The calculator uses the following formulas to estimate learning retention:

Retention Rate:

\\[ R_r = \min\left(100 \cdot \frac{S_t \cdot R_f \cdot M_l}{C_m}, 100\right) \\]

Knowledge Decay:

\\[ K_d = \min\left(100 \cdot \frac{C_m}{S_t \cdot R_f \cdot M_l}, 100\right) \\]

Study Efficiency:

\\[ E_s = \min\left(100 \cdot \frac{S_t \cdot M_l}{C_m \cdot (1 / R_f)}, 100\right) \\]

Where:

\\( R_r \\): Retention rate (%)
\\( S_t \\): Study time multiplier (\\( \sqrt{S_h / 10} \\), where \\( S_h \\) is study hours)
\\( R_f \\): Review frequency multiplier (Rare: 0.7, Regular: 1.0, Frequent: 1.3)
\\( M_l \\): Learning method multiplier (Reading: 0.8, Active Recall: 1.0, Spaced Repetition: 1.2)
\\( C_m \\): Material complexity multiplier (Simple: 0.8, Moderate: 1.0, Complex: 1.2)
\\( K_d \\): Knowledge decay (%)
\\( E_s \\): Study efficiency (%)

Example Calculations

Example 1: Short Study, Frequent Review, Simple Material, Spaced Repetition

Input: Study Time = 5 hours, Review Frequency = Frequent, Material Complexity = Simple, Learning Method = Spaced Repetition

\\[ S_t = \sqrt{S_h / 10} = \sqrt{5 / 10} = 0.707 \\] \\[ R_r = \min\left(100 \cdot \frac{S_t \cdot R_f \cdot M_l}{C_m}, 100\right) = \min\left(100 \cdot \frac{0.707 \cdot 1.3 \cdot 1.2}{0.8}, 100\right) = 100 \ \% \\] \\[ K_d = \min\left(100 \cdot \frac{C_m}{S_t \cdot R_f \cdot M_l}, 100\right) = \min\left(100 \cdot \frac{0.8}{0.707 \cdot 1.3 \cdot 1.2}, 100\right) = 72.45 \ \% \\] \\[ E_s = \min\left(100 \cdot \frac{S_t \cdot M_l}{C_m \cdot (1 / R_f)}, 100\right) = \min\left(100 \cdot \frac{0.707 \cdot 1.2}{0.8 \cdot (1 / 1.3)}, 100\right) = 100 \ \% \\]

Result: Retention Rate: 100%, Knowledge Decay: 72.45%, Study Efficiency: 100%

Example 2: Moderate Study, Regular Review, Moderate Material, Active Recall

Input: Study Time = 20 hours, Review Frequency = Regular, Material Complexity = Moderate, Learning Method = Active Recall

\\[ S_t = \sqrt{S_h / 10} = \sqrt{20 / 10} = 1.414 \\] \\[ R_r = \min\left(100 \cdot \frac{S_t \cdot R_f \cdot M_l}{C_m}, 100\right) = \min\left(100 \cdot \frac{1.414 \cdot 1.0 \cdot 1.0}{1.0}, 100\right) = 100 \ \% \\] \\[ K_d = \min\left(100 \cdot \frac{C_m}{S_t \cdot R_f \cdot M_l}, 100\right) = \min\left(100 \cdot \frac{1.0}{1.414 \cdot 1.0 \cdot 1.0}, 100\right) = 70.71 \ \% \\] \\[ E_s = \min\left(100 \cdot \frac{S_t \cdot M_l}{C_m \cdot (1 / R_f)}, 100\right) = \min\left(100 \cdot \frac{1.414 \cdot 1.0}{1.0 \cdot (1 / 1.0)}, 100\right) = 100 \ \% \\]

Result: Retention Rate: 100%, Knowledge Decay: 70.71%, Study Efficiency: 100%

Example 3: Long Study, Rare Review, Complex Material, Reading

Input: Study Time = 50 hours, Review Frequency = Rare, Material Complexity = Complex, Learning Method = Reading

\\[ S_t = \sqrt{S_h / 10} = \sqrt{50 / 10} = 2.236 \\] \\[ R_r = \min\left(100 \cdot \frac{S_t \cdot R_f \cdot M_l}{C_m}, 100\right) = \min\left(100 \cdot \frac{2.236 \cdot 0.7 \cdot 0.8}{1.2}, 100\right) = 100 \ \% \\] \\[ K_d = \min\left(100 \cdot \frac{C_m}{S_t \cdot R_f \cdot M_l}, 100\right) = \min\left(100 \cdot \frac{1.2}{2.236 \cdot 0.7 \cdot 0.8}, 100\right) = 95.69 \ \% \\] \\[ E_s = \min\left(100 \cdot \frac{S_t \cdot M_l}{C_m \cdot (1 / R_f)}, 100\right) = \min\left(100 \cdot \frac{2.236 \cdot 0.8}{1.2 \cdot (1 / 0.7)}, 100\right) = 87.25 \ \% \\]

Result: Retention Rate: 100%, Knowledge Decay: 95.69%, Study Efficiency: 87.25%

Formulas Used in Learning Retention Rate Calculator

Example Calculations

Related To Learning Retention Rate Calculator