# Patient Satisfaction Score Calculator

> Score a 5-point patient satisfaction question: top-box and top-two-box percentages, mean score and a Wilson confidence interval for the top-box rate.

Category: Healthcare operations · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/patient-satisfaction-score-calculator

Enter how many patients chose each answer on a 1–5 scale. Top-box scoring counts only the best answer; the confidence interval shows how much the score could move with a different sample.

Also called: Top-box score calculator, Patient survey calculator.

## Inputs
- 5 (very satisfied) (unit responses; default 50; optional)
- 4 (satisfied) (unit responses; default 35; optional)
- 3 (neutral) (unit responses; default 10; optional)
- 2 (dissatisfied) (unit responses; default 3; optional)
- 1 (very dissatisfied) (unit responses; default 2; optional)
- Confidence level (options: 90%, 95%, 99%; default 95)

## Results
- Top-box score (5s)
- Top-box interval: lower
- Top-box interval: upper
- Top-two-box (4s and 5s)
- Bottom-two-box (1s and 2s)
- Mean score (1–5)
- Responses

## Formula

```
Top box = n₅ ÷ n;  Mean = Σ k·nₖ ÷ n;  Wilson interval = [p + z²/2n ± z√(p(1−p)/n + z²/4n²)] ÷ (1 + z²/n)
```

Where:
- nₖ: number of responses scoring k
- n: total responses
- p: top-box proportion
- z: 1.645, 1.960 or 2.576 for 90%, 95% or 99% confidence

## Worked example
1. n = 50 + 35 + 10 + 3 + 2 = 100; top box = 50 ÷ 100 = 50%; top two = 85%.
2. Mean = (5×50 + 4×35 + 3×10 + 2×3 + 1×2) ÷ 100 = 4.28.
3. Wilson 95% interval for 50 of 100: 40.4% to 59.6%.

**Result:** Half of 100 patients gave the top score; the true top-box rate is plausibly between about 40% and 60%.

## What the result means

Top-box scores are more sensitive to change than means, which bunch near the top of the scale. Wide intervals mean small samples: avoid ranking clinicians or units whose intervals overlap heavily.

## Assumptions and limits
- Responses are a random sample of patients and are independent.
- The interval is for the top-box rate only.
- No adjustment for patient mix or survey mode, which official programmes such as HCAHPS apply.
- Non-response bias is not addressed: patients who reply may differ from those who do not.

## Questions

### Why use top-box rather than the mean?

The mean treats the scale as evenly spaced and hides the share of truly delighted patients. Top-box is easy to explain and to track over time.

### Why a Wilson interval?

It behaves well for small samples and for rates near 0% or 100%, where the simple normal approximation gives impossible limits.

## Related calculators
- [Confidence Interval Calculator](https://calculators.geekmidst.com/calculators/confidence-interval-calculator)
- [Sample Size Calculator](https://calculators.geekmidst.com/calculators/sample-size-calculator)
- [Percentage Calculator](https://calculators.geekmidst.com/calculators/percentage-calculator)
- [Patient Appointment Lead Time Calculator](https://calculators.geekmidst.com/calculators/patient-appointment-lead-time-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/patient-satisfaction-score-calculator