Dose converters

If you would like to skip the theory, links to dose converters are at the bottom of this page.

LQ model used

This tool uses linear-quadratic (LQ) approach to calculate biologically equivalent dose (BED). Isoeffective dose is described by the following equation:

  biologically equivalent dose conversion in linear quadratic model (1)

where d and D are fractional and total dose for the treatment. The following tables can be used for the α / β ratios for normal tissues:

Table 1: α to β ratios for normal tissues, date compiled from Basic Clinical Radiobiology
Early reactions Late reactions
Organ/reaction α / β, Gy
Skin, desquamation
Jejunum, clones 6.0-10.7
Colon, weight loss
Testis, clones 12-13
Tumor bed 5.6-6.8
Oral mucosa, mucositis 8-15
Organ/reaction α / β, Gy
Spinal cord, cervical
Colon, weight loss 3.1-5.0
Kidney (animal studies) 0.5-4.3
Lung, Pneumonitis
Bladder, frequency capacity 5-10
Skin, vasculature 2.6-2.8
Subcutis, fibrosis 1.7
Breast 3.1-3.4
Nerve, optic neuropathy
      Brachial plexopathy
Bowel 3.9-4.3
Head and Neck, various 3.5-4.0
Supraglottic larynx, various 3.8
Oral Cavity + oropharynx

The α / β for well-oxygenated carcinomas of head and neck, and lung, are thought to be similar or, sometimes higher, than for early-responding normal tissues. Some human tumour types such as melanoma and sarcomas may exhibit low α / β ratios; and early-stage prostate and breast cancer may have α / β ratios perhaps even lower than for late reactions (of normal tissues). Please, find some α / β ratios in the table below:

Table 2: α to β ratios for tumors
Tumor α / β, Gy
Head and Neck, various
      Vocal cord
      Buccal mucosa
Skin 8.5
Prostate 1.1
Breast 4.6
Oesophagus 4.9
Melanoma 0.6
Liposarcoma 0.4

For more details you can use, for example, Basic Clinical Radiobiology by Joiner and Kogel, or earlier, Steel's editions.

Often α / β = 10 Gy is used for tumor and α / β = 3 Gy is used for normal tissues if better estimates are not available.

The LQ model is not applicable for hypofractionated treatments. Also, formula (1) does not include certain factors, such as incomplete repair or proliferation.

Biologically equivalent dose

Above we described how to convert one dose regiment to the other but failed to explain what is BED. BED is the theoretical limit of the equivalent dose delivered in small fraction, i.e. when complete repair takes place. The following formula gives BED:

  biologically equivalent or isoeffective dose (2)


Another measure commonly used is equivalent dose in 2 Gy fractions, EQD2, which is given by D2 in formula (1) with d2 = 2 Gy.

Dose converters:

There are, actually, two dose converters, one is used when you know new dose per fraction and would like to calculate equivalent number of fractions, and the other is used when you know new number of fractions and need to calculate new dose.

New number of fractions based on new dose per fraction

New dose per fraction based on new number of fractions

Disclaimer: This page is intended for educational purposes only. Any error resulting from misuse of this software is a sole responsibility of the user.