BED Calculator

Convert a radiotherapy fractionation schedule into its biologically effective dose (BED) and EQD2 using the linear-quadratic model.

Quick Facts

Formula
BED = n × d × (1 + d/(α/β))
Linear-quadratic model. EQD2 = BED / (1 + 2/(α/β)). Typical α/β is about 10 Gy for tumors and early-responding tissue, about 3 Gy for late-responding tissue.

Your Results

Calculated
Biologically effective dose
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BED in Gy
Total physical dose
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n × d in Gy
EQD2
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Equivalent dose in 2 Gy fractions
Relative effectiveness
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RE = 1 + d/(α/β)

Ready

Enter fractions, dose per fraction, and alpha/beta, then calculate.

Understanding Biologically Effective Dose (BED)

Biologically effective dose (BED) is a radiobiology quantity from the linear-quadratic (LQ) model that expresses the biological impact of a radiotherapy course independent of how it is split into fractions. Two schedules with the same total physical dose can produce different biological effects because a larger dose per fraction carries more weight. BED captures that difference so schedules can be compared on equal footing.

The formula

For a course of n fractions delivering d gray (Gy) each, with a tissue-specific alpha/beta ratio α/β, the calculator reports three values:

  • BED = n × d × (1 + d/(α/β)) — the total dose n×d multiplied by the relative effectiveness factor (1 + d/(α/β)).
  • Total physical dose = n × d — the raw prescribed dose in Gy, before any biological weighting.
  • EQD2 = BED / (1 + 2/(α/β)) — the equivalent dose in 2 Gy fractions, a common scale for comparing schedules.

Choosing the alpha/beta ratio

The α/β ratio describes how sensitive a tissue is to fraction size. Tumors and early-responding (acute) tissues are commonly modeled around 10 Gy, while late-responding normal tissues are commonly modeled around 3 Gy; prostate tumors are often taken near 1.5 Gy. Use the value appropriate to the tissue you are evaluating, and report BED with its ratio (for example, writing "BED10" when α/β = 10 Gy).

When to consult a professional

This tool performs the standard LQ-model arithmetic for education and cross-checking. Real radiotherapy decisions depend on the specific tissue, treatment volume, dose-rate effects, and individual patient factors that a generic formula cannot capture — always confirm any clinical dose calculation with a qualified radiation oncologist or medical physicist.

Frequently Asked Questions

What is the BED formula?
Biologically effective dose uses the linear-quadratic model: BED = n × d × (1 + d/(α/β)), where n is the number of fractions, d is the dose per fraction in gray (Gy), and α/β is the tissue-specific ratio. It expresses the total dose adjusted for how fractionation changes the biological effect.
What is EQD2 and how does it relate to BED?
EQD2 is the equivalent dose delivered in 2 Gy fractions. It is derived from BED as EQD2 = BED / (1 + 2/(α/β)). EQD2 lets you compare different fractionation schedules on a common 2 Gy-per-fraction scale.
What alpha/beta ratio should I use?
Common textbook values are about 10 Gy for tumors and early-responding (acute) tissues and about 3 Gy for late-responding normal tissues; prostate tumors are often modeled near 1.5 Gy. The correct value depends on the tissue, so this calculator lets you enter your own.