Calculators · Radiation Oncology · Formula

BED and EQD2 (linear-quadratic model)

Also called biologically effective dose, EQD2, equivalent dose in 2 Gy fractions, LQ model

Converts a fractionation schedule to biologically effective dose and its 2-Gy-per-fraction equivalent for a chosen α/β.

Gy
Gy

Typical: most tumours and early-reacting tissue 10; late-reacting tissue 3; CNS/kidney 2; prostate 1.5–2; breast 4.

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Formula and scoring

BED = n·d × [1 + d/(α/β)]. EQD2 = BED ÷ [1 + 2/(α/β)] = n·d × (d + α/β) ÷ (2 + α/β).

Exam and ward pearls

  • Low α/β tissues (late-reacting, prostate) are most sensitive to fraction size — the rationale for hypofractionation in prostate and breast cancer.
  • Do not confuse BED (biologically effective dose) with "biologically equivalent dose"; BED values are much larger than physical dose.

When not to rely on it

  • Use with caution for very large doses per fraction (SBRT/SRS); this calculation also ignores overall treatment time (repopulation) and incomplete repair between fractions.

Source

  1. Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62(740):679-94. doi:10.1259/0007-1285-62-740-679 · PMID 2670032
  2. Fowler JF. 21 years of biologically effective dose. Br J Radiol. 2010;83(991):554-68. doi:10.1259/bjr/31372149 · PMID 20603408

Formula and cut-offs checked against these sources on 8 Nov 2026. Educational tool for clinicians; it does not replace clinical judgement.

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