BED Calculator — Biologically Effective Dose
Convert any radiotherapy fractionation schedule into its Biologically Effective Dose (BED) and 2 Gy-equivalent (EQD2) using the linear-quadratic model.
Gy
Tissue α/β preset
Gy
BED = n × d × (1 + d / (α/β))
- 1
Total physical dose
30 × 2 Gy = 60 Gy - 2
Fraction-size correction factor
1 + 2 ÷ 10 = 1.2Larger fractions relative to α/β increase biological damage beyond the physical dose. - 3
Biologically Effective Dose (BED)
60 × 1.2 = 72 Gy
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BED = n × d × (1 + d/(α/β)) converts a fractionation schedule into a biologically meaningful dose. EQD2 = BED ÷ (1 + 2/(α/β)) expresses it as a 2 Gy/fraction equivalent for clinical comparison. Use α/β ≈ 10 Gy for tumours/early tissue, ≈ 3 Gy for late-responding tissue, ≈ 1.5 Gy for prostate.
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How this is calculated
The linear-quadratic (LQ) model translates a fractionation schedule — defined by the dose per fraction d and the number of fractions n — into a single Biologically Effective Dose (BED) that reflects the actual biological damage delivered to a specific tissue type. The tissue-specific α/β ratio is the key parameter: early-responding tissues and most tumours have α/β ≈ 10 Gy, meaning biological damage scales mainly with total dose; late-responding tissues (spinal cord, lungs, kidneys) have α/β ≈ 3 Gy, making them proportionally more sensitive to large fractions; prostate cancer is atypically low at ≈ 1.5 Gy, which is the radiobiological basis for hypofractionated prostate protocols.
EQD2 (Equivalent Dose in 2 Gy Fractions) converts any BED back into the conventional 2 Gy/fraction equivalent for the same tissue type. This lets clinicians compare schedules numerically and sum sequential radiation courses to keep organs-at-risk within tolerance constraints. EQD2 = BED ÷ (1 + 2/(α/β)).
This tool is a planning and educational aid. The LQ model has well-documented limitations at very large fractions (SBRT/SABR > 6–8 Gy/fraction), where some investigators apply correction factors. Clinical decisions require a qualified radiation oncologist who accounts for tumour geometry, organ constraints, treatment interruptions, and patient-specific biology not captured by the LQ formula alone.
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The α/β ratio characterises how sensitive a tissue is to fraction size. Use ≈10 Gy for most tumours and acutely responding tissues; ≈3 Gy for late-responding tissues; ≈1.5 Gy for prostate cancer. If you have a published tissue-specific value, enter it in the custom field. Selecting the wrong α/β will give numerically incorrect BED and EQD2 values.
BED is the absolute biological dose for a given α/β. EQD2 converts BED into the equivalent dose if it had been delivered in 2 Gy fractions for the same tissue, making it possible to add doses from different courses and compare schedules. EQD2 is the more clinically useful number for cumulative-dose calculations.
The LQ model is generally accepted for fraction sizes up to about 6–8 Gy. For larger SBRT/SABR fractions it tends to overestimate BED relative to observed tumour control, and modified models (e.g., the universal survival curve) may be preferred. Always interpret high-fraction BED values cautiously and consult published SBRT tolerance data.
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TG we-Calculate Editorial Team. (2026). BED Calculator — Biologically Effective Dose [Online calculator]. TG we-Calculate. https://we-calculate.com/ga/calculator/bed-calculator
TG we-Calculate Editorial Team. "BED Calculator — Biologically Effective Dose." TG we-Calculate. 2026. https://we-calculate.com/ga/calculator/bed-calculator.
TG we-Calculate Editorial Team, "BED Calculator — Biologically Effective Dose," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/ga/calculator/bed-calculator
@misc{wecalculate_bed_calculator, title = {BED Calculator — Biologically Effective Dose}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/ga/calculator/bed-calculator}}, year = {2026}, note = {TG we-Calculate} }
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