THE NUMBERS, EXPLAINED
How to use this calculator.
Applies your explicit scoring rules to the total question count. Bounds allow every question to have whichever outcome gives the lowest or highest score. No automatic floor at zero is applied.
Start with your inputs
Enter correct answers, wrong answers, omitted answers, reward per correct, penalty per wrong, score per omitted. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Correct answers | 30 |
| Wrong answers | 10 |
| Omitted answers | 10 |
| Reward per correct | 2 |
| Penalty per wrong | 0.5 |
| Score per omitted | 0 |
A worked example
With the example inputs above, raw score is 55. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Raw score
(30) × (2)-(10) × (0.5)+(10) × (0) = 55
Minimum possible score
((30)+(10)+(10)) × min((2),-(0.5),(0)) = -25
Maximum possible score
((30)+(10)+(10)) × max((2),-(0.5),(0)) = 100
| Result | Example answer |
|---|---|
| Raw score | 55 |
| Minimum possible score | -25 |
| Maximum possible score | 100 |
How this is calculated
Raw score
a × d-b × e+c × f
Minimum possible score
(a+b+c) × min(d,-e,f)
Maximum possible score
(a+b+c) × max(d,-e,f)
Symbols and units
- a
- Correct answers
- b
- Wrong answers
- c
- Omitted answers
- d
- Reward per correct
- e
- Penalty per wrong
- f
- Score per omitted
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
min(x, y, …) selects the smallest value.
max(x, y, …) selects the largest value.
Assumptions and limits
Applies your explicit scoring rules to the total question count. Bounds allow every question to have whichever outcome gives the lowest or highest score. No automatic floor at zero is applied.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Raw score; Minimum possible score; Maximum possible score. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Applies your explicit scoring rules to the total question count. Bounds allow every question to have whichever outcome gives the lowest or highest score. No automatic floor at zero is applied.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
OpenStax: algebra and proportional reasoning ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →