Biologically Effective Dose Calculator (BED and EQD2, linear-quadratic model)

Understanding the biologically effective dose calculator — concept and principle

This calculator computes the biologically effective dose (BED) and the equivalent dose in 2 Gy fractions (EQD2) for a radiotherapy schedule using the linear-quadratic model. It also shows the total physical dose and the relative effectiveness factor. It is intended for radiobiology education: students, physicists and trainees comparing fractionation schedules.

Bigger fractions count for more — with the default inputs: BED 75.7 Gy.

How it is calculated

BED = n × d × (1 + d ÷ (α/β))
EQD2 = BED ÷ (1 + 2 ÷ (α/β))
Total physical dose = n × d
Relative effectiveness = 1 + d ÷ (α/β)

n = number of fractions, d = dose per fraction (Gy), α/β = tissue-specific ratio (Gy).

The principle

In the linear-quadratic model, radiation kills cells through a component proportional to dose (α) and one proportional to dose squared (β). Large fractions therefore have more effect per gray than small ones. The α/β ratio expresses how sensitive a tissue is to fraction size: late-reacting normal tissues have low ratios, around 3 Gy, so they benefit more from small fractions, while many tumours and early-reacting tissues have higher ratios, around 10 Gy. BED puts different schedules on one scale; EQD2 expresses it as the dose that would have the same effect in conventional 2 Gy fractions.

Worked example

Defaults: 15 fractions of 2.67 Gy; α/β = 3 Gy.

Total physical dose = 15 × 2.67 = 40.05 Gy, shown as 40.
Relative effectiveness = 1 + 2.67 ÷ 3 = 1.89.
BED = 40.05 × 1.89 = 75.7 Gy.
EQD2 = 75.7 ÷ (1 + 2 ÷ 3) = 75.7 ÷ 1.667 = 45.4 Gy.

Each point is the calculator re-run with only “Dose per fraction, d (Gy)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Dose per fraction, d (Gy)	Biologically effective dose, BED (Gy)
0.667	12.2
1.33	28.9
2	50.1
2.67	75.7
3.34	105.8
4	140.3
5.34	222.7

How to read the result

For a late-reacting tissue with α/β = 3, this 15-fraction schedule is roughly equivalent to 45.4 Gy in 2 Gy fractions. Changing α/β to 10 shows the tumour-equivalent dose. Comparing EQD2 values across schedules helps explain why hypofractionated regimens can match conventional ones.

Common mistakes

Using a single α/β for all tissues.
Ignoring overall treatment time and tumour repopulation.
Applying the simple model to very large doses per fraction, where it is less reliable.
Comparing BED values calculated with different α/β ratios.

Keep in mind: For education only. This must not be used for treatment planning; real plans are made by radiation oncologists and medical physicists.

Frequently asked questions

What is EQD2?

The total dose in 2 Gy fractions that would give the same biological effect as the schedule entered.

What α/β ratio should I use?

Commonly about 3 Gy for late effects and about 10 Gy for many tumours, but values vary by tissue.

Why is BED higher than the physical dose?

Because each fraction is larger than the reference, adding extra effect per gray.

Sources: Fowler JF, "The linear-quadratic formula and progress in fractionated radiotherapy", Br J Radiol 1989;62:679–694

Checked 9 Nov 2026. Linear-quadratic model as formulated by Fowler JF, “The linear-quadratic formula and progress in fractionated radiotherapy”, Br J Radiol 1989;62:679–694 (BED = nd[1 + d/(α/β)]; EQD2 conversion); typical α/β values of about 3 and 10 Gy are standard values.

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