# BED and EQD2 Calculator (Radiotherapy)

URL: https://speedycalculator.com/calculators/health/bed/
Last updated: 2026-10-30

> The BED calculator works out the biologically effective dose and the equivalent dose in 2 Gy fractions (EQD2) of a radiotherapy schedule from the number of fractions, dose per fraction and the tissue's α/β ratio, so different schedules can be compared.

## Inputs

- Number of fractions
- Dose per fraction (Gy)
- α/β ratio (Gy)

## Results

- Total physical dose
- Biologically effective dose
- EQD2
- BED for late tissues (α/β 3)

## Formula

```
BED = n × d × (1 + d ÷ (α/β))
EQD2 = BED ÷ (1 + 2 ÷ (α/β))
α/β ≈ 10 Gy for tumours and early-reacting tissues, ≈ 3 Gy for late-reacting tissues (≈ 1.5 for prostate cancer)
```

## Explanation

The linear-quadratic model explains why the same total dose has different effects when given in fewer, larger fractions. BED and EQD2 let radiation oncologists compare conventional, hypofractionated and stereotactic schedules.

### How to use the BED and EQD2 Calculator

- **Number of fractions**
- **Dose per fraction**
- **α/β ratio**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the number of fractions, the dose per fraction and the α/β ratio.

### Tips

- Keep a record of your imaging and its doses.
- Ask whether an ultrasound or MRI could answer the question without radiation.
- Tell staff if you might be pregnant.
- Background radiation varies by altitude and region.

### Common mistakes to avoid

- Comparing mSv (effective dose) with mGy (absorbed dose).
- Assuming every scan of the same type gives the same dose.
- Ignoring cumulative dose from repeated scans.

### Inputs explained

FieldWhat to enterNumber of fractionsA numberDose per fractionIn Gyα/β ratioIn Gy

### What each result means

- **Total physical dose** = [Number of fractions]×[Dose per fraction]
- **Biologically effective dose** = [Number of fractions]×[Dose per fraction]×(1 + [Dose per fraction]÷[α÷β ratio])
- **EQD2** = [Biologically effective dose]÷(1 + 2÷[α÷β ratio])
- **BED for late tissues (α/β 3)** = [Number of fractions]×[Dose per fraction]×(1 + [Dose per fraction]÷3)

### Example values

How the main result changes when **Number of fractions** changes and everything else stays at the example values above:

Number of fractionsBiologically effective dose (Gy)1035.11552.62070.12587.730105.240140.3
*Health note: this calculator is for education and screening only and is not a diagnosis or treatment advice. Discuss your results with a qualified clinician.*

## Worked example

Inputs — Number of fractions: 20; Dose per fraction: 2.75 Gy; α/β ratio: 10 Gy.

Results — Total physical dose = 55 Gy; **Biologically effective dose = 70.1 Gy**; EQD2 = 58.4 Gy; BED for late tissues (α/β 3) = 105.4 Gy.

## Key terms

- **BED**: Biologically effective dose.
- **EQD2**: Equivalent dose in 2 Gy fractions.

## FAQ

**What is EQD2?**
The dose in 2 Gy fractions that would have the same biological effect.

**Why does α/β matter?**
Tissues with low α/β are more sensitive to large fractions.

**Does BED account for treatment time?**
Not in this basic form; repopulation corrections exist for long treatments.


## Sources

- [Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol, 1989](https://pubmed.ncbi.nlm.nih.gov/2670032/)