THE NUMBERS, EXPLAINED
How to use this calculator.
Each query contributes reciprocal rank of its first relevant result; zero denotes no relevant result. All queries have equal weight.
Start with your inputs
Enter first relevant rank per query (0 means none). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| First relevant rank per query (0 means none) | 1,2,0,4 |
A worked example
With the example inputs above, mean reciprocal rank is 0.4375. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Mean reciprocal rank | 0.4375 |
| Queries with a relevant result (%) | 75 |
| First-place result share (%) | 25 |
How this is calculated
Mean reciprocal rank
Average reciprocal ranks, assigning zero to unanswered queries.
Queries with a relevant result (%)
Divide queries with a positive rank by all queries.
First-place result share (%)
Divide rank-one queries by all queries.
Symbols and units
- a
- First relevant rank per query (0 means none)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Each query contributes reciprocal rank of its first relevant result; zero denotes no relevant result. All queries have equal weight.
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?
Mean reciprocal rank; Queries with a relevant result (%); First-place result share (%). 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: Each query contributes reciprocal rank of its first relevant result; zero denotes no relevant result. All queries have equal weight.
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
Microsoft Research SIGIR paper — Reciprocal Rank and Mean Reciprocal Rank definitions ↗
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 →