Free Tool

QALY Calculator

Calculate quality-adjusted life years (QALYs) for two scenarios from the utility and duration of each health state, with or without discounting, and see the QALYs gained by the new scenario.

The calculator opens with the hypothetical worked example below.

Default 3.5%. Enter 0 for no discounting. First year undiscounted.

Scenario A · comparator

Health state 1

Health state 2

2 of 6 states · utility −0.594 to 1

Scenario B · new

Health state 1

Health state 2

2 of 6 states · utility −0.594 to 1

Results

ScenarioUndiscounted QALYsDiscounted QALYs
Current care1.5501.513
New treatment2.5002.405
QALYs gainedNew treatment minus Current care0.9500.892

Discounted at 3.5% a year; the first year is not discounted and partial years count pro rata. Totals cover 2.5 years for Current care and 3.5 years for New treatment.

Show the calculation for each health state

Current care

Health stateYearsUtilityUndiscountedDiscounted
Stable disease0–1.50.71.0501.038
Progressed disease1.5–2.50.50.5000.475

New treatment

Health stateYearsUtilityUndiscountedDiscounted
Stable disease0–2.50.82.0001.946
Progressed disease2.5–3.50.50.5000.459

Educational tool. This calculator is for learning and quick checks. It is not a substitute for a full economic model, which handles time, uncertainty and the methods an HTA body requires, or for an HTA submission. Calculations run in your browser and the numbers you enter are not stored.

Method

How the calculation works

A QALY combines length and quality of life in one number: one year in full health counts as 1 QALY, and a year in a health state with a utility of 0.5 counts as 0.5 QALYs. Each health state contributes its utility multiplied by the time spent in it.

QALYs = Σi (ui × di)
Discounted QALYs = Σi ui × Σt yi,t ÷ (1 + r)t − 1
ui
Utility of health state i, on a scale where 1 is full health and 0 is a state equivalent to being dead. Negative values describe states valued as worse than dead. This calculator accepts −0.594 to 1.
di
Time spent in health state i, in years. States follow one another: the first starts at year 0, the next when the previous one ends.
yi,t
The part of year t (the interval from t − 1 to t) spent in state i, between 0 and 1.
r
Annual discount rate, for example 0.035 for 3.5%. With r = 0, discounted and undiscounted QALYs are equal.

Discounting convention used on this page

Annual discounting with the first year undiscounted. Time is split into years counted from the start of the analysis: year 1 runs from 0 to 1, year 2 from 1 to 2, and so on. Year t (t = 1, 2, 3, …) is weighted by 1 ÷ (1 + r)t − 1, and partial years count pro rata. The first year therefore has a weight of 1, the second 1 ÷ (1 + r), the third 1 ÷ (1 + r)², and so on.

QALYs gained are the QALYs of scenario B minus those of scenario A, worked out separately for undiscounted and discounted values. The same convention is used in the discounting calculator, and the QALYs gained can be fed into the ICER calculator.

Worked example

Worked example (hypothetical)

Current care: 1.5 years with stable disease (utility 0.7), then 1 year with progressed disease (utility 0.5). New treatment: 2.5 years with stable disease (utility 0.8), then 1 year with progressed disease (utility 0.5). Discount rate 3.5% a year. All values are hypothetical and are the default inputs of the calculator above.

Undiscounted

  • Current care: 0.7 × 1.5 + 0.5 × 1 = 1.05 + 0.5 = 1.550 QALYs
  • New treatment: 0.8 × 2.5 + 0.5 × 1 = 2.0 + 0.5 = 2.500 QALYs
  • QALYs gained: 2.500 − 1.550 = 0.950

Discounted at 3.5%

Year weights: year 1 = 1, year 2 = 1 ÷ 1.035 = 0.9662, year 3 = 1 ÷ 1.035² = 0.9335, year 4 = 1 ÷ 1.035³ = 0.9019.

  • Current care, stable (years 0 to 1.5): 0.7 × (1 + 0.5 × 0.9662) = 1.038
  • Current care, progressed (1.5 to 2.5): 0.5 × (0.5 × 0.9662 + 0.5 × 0.9335) = 0.475
  • Current care total: 1.038 + 0.475 = 1.513 QALYs
  • New treatment, stable (0 to 2.5): 0.8 × (1 + 0.9662 + 0.5 × 0.9335) = 1.946
  • New treatment, progressed (2.5 to 3.5): 0.5 × (0.5 × 0.9335 + 0.5 × 0.9019) = 0.459
  • New treatment total: 1.946 + 0.459 = 2.405 QALYs
  • QALYs gained: 2.405 − 1.513 = 0.892

Discounting reduces the gain from 0.950 to 0.892 QALYs because the extra benefit of the new treatment arrives in later years, which carry lower weights.

In practice

How HTA bodies use this

HTA bodies that use cost-utility analysis measure health benefit in QALYs and compare technologies by the cost per QALY gained. Utilities usually come from a generic preference-based questionnaire such as the EQ-5D, converted to utilities with a country-specific value set; check the methods guide of the agency you work with for its preferred instrument and value set. QALYs are discounted at the rate that guide sets, and the discounting calculator lists published rates with links to their sources.

In a submission, QALYs do not come from fixed durations. They come from an economic model, such as a Markov or partitioned survival model, that follows a cohort through health states cycle by cycle, accounts for mortality and applies within-cycle corrections. This calculator shows the arithmetic underneath those models.

Utilities, QALYs and where the numbers come from are covered in Module 6: Measuring Health Outcomes, and discounting in Module 5: Health Economics Fundamentals.

FAQ

Frequently asked questions

Multiply the utility of each health state by the number of years spent in it and add the results. For example, 2 years at a utility of 0.75 gives 1.5 QALYs. To discount, weight the time spent in year t by 1 ÷ (1 + r)^(t − 1), where r is the annual discount rate, so the first year is not discounted.

Yes. Some value sets include health states that people value as worse than being dead, which gives negative utilities. The worst state in the UK EQ-5D-3L value set is valued at −0.594, which is the lower limit used in this calculator. Other value sets have different minimum values.

HTA guidelines ask for future costs and health effects to be converted to present values so that options whose benefits arrive at different times can be compared on the same basis. The rate depends on the guideline: some use the same rate for costs and health effects, others use a lower rate for health effects.

Time is split by year and partial years count pro rata. A health state that runs from year 1.5 to year 2.5 spends half a year in year 2, weighted by 1 ÷ (1 + r), and half a year in year 3, weighted by 1 ÷ (1 + r)².

Economic models usually run in cycles, often monthly or yearly, track mortality and movement between health states, apply a half-cycle or other within-cycle correction, and may discount by cycle or continuously. This calculator uses fixed durations and simple annual discounting, so small differences are expected.

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Go further

Understand Where QALYs Come From

The HTA Course explains utilities, the EQ-5D, QALYs, discounting and the models that turn them into a cost per QALY, in 15 modules and 79 self-paced lessons.