LQL-Equiv: free online EQD2, BED, NTCP and TCP calculator for radiotherapy
Cyril Voyant · Updated 2026-10-18
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Free, no installation. Runs entirely in your browser: nothing you enter leaves the page.
Biologically equivalent doses in radiotherapy, under the linear-quadratic-linear model. LQL-Equiv computes the biologically effective dose (BED), the equivalent dose in a reference fractionation (EQD2 and others), the normal-tissue complication probability (NTCP), the tumour control probability (TCP) and the radiation-induced cancer risk. It handles successive treatment courses separated by gaps, two fractions a day, accelerated proliferation and overall treatment time.
For research and education only. Not a medical device. Outputs must not be used to choose or modify a prescription, to compensate a real interruption, to sum dose for a reirradiation decision, or to predict a probability for an individual patient. NTCP and TCP are model illustrations that have never been validated against clinical outcome.
Validated against the original, case by case
Version 3.0 is a complete reimplementation of the 2014 MATLAB application. The 2014 software was run over 4,438 treatment schedules: every organ/tumour pair, a wide fractionation grid, gaps, twice-daily schedules and random multi-course plans.
| Values compared | 69,131 |
| Agreeing at the 2014 output precision | 69,125 (99.991%) |
| Cases differing | 2 of 4,438, both exact ties of the 2014 search grid |
Sixteen analytical checks that do not rely on the 2014 code (continuity at the transition dose, EQD = n·d at the reference fraction size, additivity, round trip) test whether the calculation itself is right. One of them revealed the only change that moves a number: overall time is now counted once instead of twice. The 2014 behaviour stays available for recomputing older results.
What it covers
- 34 organs at risk and 20 tumour sites, each parameter with its documented provenance.
- Linear-quadratic model with a linear tail above the transition dose; Dale and Van Dyk proliferation; Thames incomplete-repair correction; Lyman NTCP; logistic or Poisson TCP; linear-exponential cancer risk.
- Also a Python library with no dependency beyond the standard library:
pip install -e ., thencompute(...).
Typical uses in teaching and research
- Show students how EQD2 depends on dose per fraction and on α/β.
- Compare hypofractionated and conventional schedules on the same organ.
- Explore how a treatment gap changes the equivalent dose under the model's assumptions.
History and citation
The original LQ-Equiv (MATLAB, 2014) accompanied C. Voyant, D. Julian, R. Roustit, K. Biffi, C. Lantieri, Biological effects and equivalent doses in radiotherapy: a software solution, Reports of Practical Oncology and Radiotherapy, 2014, doi:10.1016/j.rpor.2013.08.004. Cite the current software as: C. Voyant, D. Julian, LQL-Equiv-web, doi:10.5281/zenodo.21948623.
Source code (MIT) · Full 2014 comparison · Parameter provenance · Also usable through WebSemantic, in plain language.