Language Learning Progress Calculator

Language Learning Progress Calculator estimates weeks to reach target proficiency using study frequency, duration, method, motivation, and language difficulty.

Current Proficiency Level:

Target Proficiency Level:

Study Frequency (sessions/week):

Session Duration (minutes):

Learning Method:

Motivation Level:

Language Difficulty:

Formulas Used in Language Learning Progress Calculator

The calculator uses the following formulas to estimate language learning progress:

Learning Rate:

\\[ R = M \cdot \left( \frac{F \cdot D}{60} \right) \cdot E \cdot \frac{1}{L} \\]

Time to Target:

\\[ T = \frac{P_{\text{target}} – P_{\text{current}}}{R} \\]

Progress Timeline:

\\[ P_{\text{week}} = P_{\text{current}} + R \cdot \text{week} \\]

Efficiency Score:

\\[ S = \min\left(100 \cdot \frac{R}{R_{\text{max}}}, 100\right) \\]

Where:

\\( R \\): Learning rate (proficiency points/week)
\\( M \\): Method efficiency (points/hour, Self-Study: 5, Tutor: 8, Immersion: 12)
\\( F \\): Study frequency (sessions/week)
\\( D \\): Session duration (minutes)
\\( E \\): Effort factor (Low: 0.5, Medium: 0.75, High: 1.0)
\\( L \\): Language difficulty factor (Easy: 1, Medium: 1.5, Hard: 2)
\\( T \\): Time to target proficiency (weeks)
\\( P_{\text{target}} \\): Target proficiency (points, e.g., B1: 400)
\\( P_{\text{current}} \\): Current proficiency (points)
\\( P_{\text{week}} \\): Proficiency at given week (points)
\\( S \\): Efficiency score (%)
\\( R_{\text{max}} \\): Maximum learning rate (20 points/week)

Example Calculations

Example 1: Beginner, Easy Language

Input: Current = Beginner (0 points), Target = A2 (200 points), Frequency = 3 sessions/week, Duration = 60 min, Method = Self-Study, Motivation = Low, Difficulty = Easy

\\[ R = 5 \cdot \left( \frac{3 \cdot 60}{60} \right) \cdot 0.5 \cdot \frac{1}{1} = 5 \cdot 3 \cdot 0.5 \cdot 1 = 7.5 \ \text{points/week} \\] \\[ T = \frac{200 – 0}{7.5} \approx 26.67 \ \text{weeks} \\] \\[ S = 100 \cdot \frac{7.5}{20} = 37.5 \ \% \\]

Timeline: Week 1: 7.5 points, Week 2: 15 points, Week 4: 30 points, Week 8: 60 points

Result: Learning Rate = 7.5 points/week, Time = 26.67 weeks, Efficiency = 37.5%

Example 2: Intermediate, Medium Language

Input: Current = A2 (200 points), Target = B2 (600 points), Frequency = 5 sessions/week, Duration = 60 min, Method = Tutor, Motivation = Medium, Difficulty = Medium

\\[ R = 8 \cdot \left( \frac{5 \cdot 60}{60} \right) \cdot 0.75 \cdot \frac{1}{1.5} = 8 \cdot 5 \cdot 0.75 \cdot 0.6667 \approx 20 \ \text{points/week} \\] \\[ T = \frac{600 – 200}{20} = 20 \ \text{weeks} \\] \\[ S = 100 \cdot \frac{20}{20} = 100 \ \% \\]

Timeline: Week 1: 220 points, Week 2: 240 points, Week 4: 280 points, Week 8: 360 points

Result: Learning Rate = 20 points/week, Time = 20 weeks, Efficiency = 100%

Example 3: Advanced, Hard Language

Input: Current = B1 (400 points), Target = C1 (900 points), Frequency = 7 sessions/week, Duration = 90 min, Method = Immersion, Motivation = High, Difficulty = Hard

\\[ R = 12 \cdot \left( \frac{7 \cdot 90}{60} \right) \cdot 1.0 \cdot \frac{1}{2} = 12 \cdot 10.5 \cdot 1.0 \cdot 0.5 = 63 \ \text{points/week} \\] \\[ T = \frac{900 – 400}{63} \approx 7.94 \ \text{weeks} \\] \\[ S = 100 \cdot \frac{63}{20} \approx 100 \ \% \ (\text{capped}) \\]

Timeline: Week 1: 463 points, Week 2: 526 points, Week 4: 652 points, Week 8: 904 points (capped at 900)

Result: Learning Rate = 63 points/week, Time = 7.94 weeks, Efficiency = 100%