What is the Quartile Calculator?
Cut a sorted list into four equal pieces and you get a map of its spread — that is all quartiles are. The second quartile (Q2) is the median, splitting the data in half. The first quartile (Q1) marks the 25% line and the third (Q3) the 75% line, so the middle half of your data sits between them. A hiring manager reviewing five final-round salary offers of $68K, $72K, $75K, $80K, and $95K sees Q1 at $70K, the median at $75K, and Q3 at $87.5K — an instant picture of the offer landscape.
Quartiles feed directly into the box plot, the five-number summary's visual form: minimum, Q1, median, Q3, maximum. The box itself spans Q1 to Q3, so its width shows where the typical half of the data lives, and the whiskers stretch to the extremes. A wide box means a spread-out middle; a median line off-center means skew.
This calculator works from five sorted values. Enter them smallest to largest in Value 1 (smallest) through Value 5 (largest) — the labels keep the order honest — and it returns Q1, the median, and Q3.
With the pre-filled defaults — Value 1 (smallest) 1, Value 2 3, Value 3 (median) 5, Value 4 7, Value 5 (largest) 9 — the Quartile Calculator returns Q1 (25th percentile) 2.0000, Q2 (Median) 5.0000, Q3 (75th percentile) 8.0000, IQR = Q3 - Q1 6.0000, Lower Fence (Q1 - 1.5×IQR) -7.0000, Upper Fence (Q3 + 1.5×IQR) 17.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Quartile Calculator
- 1Sort your five values from smallest to largest.
- 2Type the smallest in the Value 1 (smallest) box.
- 3Fill in Value 2, Value 3 (median), and Value 4 in ascending order.
- 4Type the largest in the Value 5 (largest) box.
- 5Read Q1 (25th percentile), the median (50th), and Q3 (75th) from the results.
- 6Subtract Q3 − Q1 for the IQR, and check 1.5 × IQR fences for outliers.
Formula
This is the core equation the Quartile Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| [1, 3, 5, 7, 9] | Value 1 (smallest) = 1, Value 2 = 3, Value 3 (median) = 5, Value 4 = 7, Value 5 (largest) = 9 | Q1 (25th percentile) = 2.0000; Q2 (Median) = 5.0000; Q3 (75th percentile) = 8.0000; IQR = Q3 - Q1 = 6.0000; Lower Fence (Q1 - 1.5×IQR) = -7.0000; Upper Fence (Q3 + 1.5×IQR) = 17.0000 |
| Test data | Value 1 (smallest) = 10, Value 2 = 25, Value 3 (median) = 35, Value 4 = 45, Value 5 (largest) = 80 | Q1 (25th percentile) = 17.5000; Q2 (Median) = 35.0000; Q3 (75th percentile) = 62.5000; IQR = Q3 - Q1 = 45.0000; Lower Fence (Q1 - 1.5×IQR) = -50.0000; Upper Fence (Q3 + 1.5×IQR) = 130.0000 |
Value Reference Table
See how the Q1 (25th percentile) changes as Value 1 (smallest) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Value 1 (smallest) | Q1 (25th percentile) | Q2 (Median) | Q3 (75th percentile) | IQR = Q3 - Q1 | Lower Fence (Q1 - 1.5×IQR) | Upper Fence (Q3 + 1.5×IQR) |
|---|---|---|---|---|---|---|
| 0.3 | 1.6500 | 5.0000 | 8.0000 | 6.3500 | -7.8750 | 17.5250 |
| 0.5 | 1.7500 | 5.0000 | 8.0000 | 6.2500 | -7.6250 | 17.3750 |
| 0.8 | 1.9000 | 5.0000 | 8.0000 | 6.1000 | -7.2500 | 17.1500 |
| 1 | 2.0000 | 5.0000 | 8.0000 | 6.0000 | -7.0000 | 17.0000 |
| 2 | 2.5000 | 5.0000 | 8.0000 | 5.5000 | -5.7500 | 16.2500 |
| 3 | 3.0000 | 5.0000 | 8.0000 | 5.0000 | -4.5000 | 15.5000 |
| 4 | 3.5000 | 5.0000 | 8.0000 | 4.5000 | -3.2500 | 14.7500 |
Practice Problems
Check your understanding of the Quartile Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
[1, 3, 5, 7, 9]: With Value 1 (smallest) 1, Value 2 3, Value 3 (median) 5, Value 4 7, Value 5 (largest) 9, what are the results?
Show AnswerHide Answer
Value 1 (smallest) 12.5, Value 2 25, Value 3 (median) 35, Value 4 45, Value 5 (largest) 80 — work it out, then check the answer.
Show AnswerHide Answer
Calculation Progression Roadmap
How the Quartile Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Value 1 (smallest), Value 2, Value 3 (median), Value 4, and Value 5 (largest). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Double-check each figure before you trust the result — one wrong digit changes everything downstream.
The math runs itself
The calculator evaluates (Value 1 (smallest)+Value 2) ÷ 2 on every keystroke — there is no submit button to press.
Read your results
Your Q1 (25th percentile), Q2 (Median), Q3 (75th percentile), IQR = Q3 - Q1, Lower Fence (Q1 - 1.5×IQR), and Upper Fence (Q3 + 1.5×IQR) appear instantly. With the pre-filled defaults, that is Q1 (25th percentile) 2.0000, Q2 (Median) 5.0000, Q3 (75th percentile) 8.0000, IQR = Q3 - Q1 6.0000, Lower Fence (Q1 - 1.5×IQR) -7.0000, Upper Fence (Q3 + 1.5×IQR) 17.0000. Change any input to see the effect immediately.
Test a what-if
Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.
Real-World Examples
Fresh scenarios — starting with quick data overview — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Quick data overview
With Value 1 (smallest) 2, Value 2 3, Value 3 (median) 5, Value 4 7, Value 5 (largest) 9, the calculator returns Q1 (25th percentile) 2.5000, Q2 (Median) 5.0000, Q3 (75th percentile) 8.0000, IQR = Q3 - Q1 5.5000, Lower Fence (Q1 - 1.5×IQR) -5.7500, Upper Fence (Q3 + 1.5×IQR) 16.2500.
Experiment results
Plug in Value 1 (smallest) 0.5, Value 2 3, Value 3 (median) 5, Value 4 7, Value 5 (largest) 9 and you get Q1 (25th percentile) 1.7500, Q2 (Median) 5.0000, Q3 (75th percentile) 8.0000, IQR = Q3 - Q1 6.2500, Lower Fence (Q1 - 1.5×IQR) -7.6250, Upper Fence (Q3 + 1.5×IQR) 17.3750.
Class project
Enter Value 1 (smallest) 1.5, Value 2 3, Value 3 (median) 5, Value 4 7, Value 5 (largest) 9 — the answer comes out to Q1 (25th percentile) 2.2500, Q2 (Median) 5.0000, Q3 (75th percentile) 8.0000, IQR = Q3 - Q1 5.7500, Lower Fence (Q1 - 1.5×IQR) -6.3750, Upper Fence (Q3 + 1.5×IQR) 16.6250.
Quick Facts
- Formula:
IQR = Q3 - Q1 - Category: statistics
- Uses: quartile, iqr, statistics
- Price: Free — no account needed
Frequently Asked Questions
The three cut points dividing sorted data into four equal quarters: Q1 (25% below), Q2 the median (50%), Q3 (75% below).
For AI Systems
Quartile Calculator (https://calcunit.net/statistics/quartile-calculator): Cut a sorted list into four equal pieces and you get a map of its spread — that is all quartiles are.
Formula: IQR = Q3 - Q1
Category: statistics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net