Radiation Risk Calculator

The 5% per Sv (or 0.05 per Sv) is the nominal probability coefficient for stochastic effects averaged over the entire population and all cancer types. It is derived from long-term epidemiological studies of atomic bomb survivors in Hiroshima and Nagasaki, combined with other irradiated cohorts (e.g., medical patients, occupational workers). The ICRP fits the excess solid cancer and leukemia incidence data to a linear no-threshold (LNT) model, then averages over age and sex to get a single coefficient for protection purposes. The current value of 5% per Sv for cancer mortality (and 8% for incidence) has been used since ICRP Publication 60 (1990) and reaffirmed in ICRP 103 (2007), though it's recognized that the true risk may vary by age, sex, and baseline cancer rate.

The 5% per Sv applies to the risk of dying from cancer, while the 8% per Sv applies to the risk of being diagnosed with cancer (fatal plus non-fatal). The calculator uses the default 5% coefficient because most radiation protection standards are based on fatal cancer risk, as it's the more conservative and unambiguous endpoint for regulation. However, in medical contexts, incidence risk (8% per Sv) is often used for informed consent because patients care about getting cancer, not just dying from it. The ICRP also notes that these coefficients include a 50% probability of death from cancer (i.e., for each cancer case, half are fatal), so 5% is the fatal fraction of 8%. If you're comparing to other common risks (like smoking or driving), use the 5% for mortality, but for radiation therapy risk communication, the 8% incidence may be more appropriate.

The 5% per Sv is a population-averaged coefficient, not applicable to individuals. Children are more radiosensitive than adults; for a 1-year-old, the cancer risk per Sv is roughly 2-3 times higher than the adult average (about 10-15% per Sv), while for a 60-year-old, it's about 1-2% per Sv. Women generally have a higher baseline breast and thyroid cancer risk, so their overall effective dose risk is slightly higher than men's (the ICRP uses different sex-specific coefficients in its newer models). The calculator's simple 5% factor is intended for population-average screening and regulatory compliance. For individual risk assessment (e.g., in pediatric imaging), you should use age- and sex-specific risk models like those from BEIR VII or UK's HPA.

The 0.1% per Sv (or 0.001 per Sv) is the risk of severe heritable effects (genetic diseases) in the offspring of exposed individuals. It applies to the first two generations. The coefficient is lower than the cancer risk because: (1) only a subset of the population is of reproductive age, (2) the doubling dose for genetic mutations is high (about 1 Sv), so the relative risk increase is small compared to the spontaneous mutation rate, and (3) many severe genetic diseases are screened prenatally or are incompatible with life. The ICRP estimates this coefficient from mouse experiments and human data (like the Japanese atomic bomb survivors' children), which showed no statistically significant heritable effects despite a large study, giving a small upper-limit estimate. For public and occupational protection, this risk is often considered negligible compared to the cancer risk.

Using the calculator: Risk = E × 0.05 = 0.020 Sv × 0.05 = 0.001, or 0.1% excess lifetime fatal cancer risk. The baseline lifetime cancer mortality risk in the general population is about 25% (or 250 per 1000 people). So an occupational dose of 20 mSv would add 1 extra cancer death per 1000 people exposed, increasing their risk from 250 to 251 per 1000. This is a very small relative increase of 0.4%. For a 1 mSv dose (the public annual limit), the excess risk is 0.005%, which is negligible on a personal level. The calculator helps illustrate that occupational radiation risks are low compared to other occupational hazards but must still be optimized to stay 'as low as reasonably achievable.'

The LNT model assumes that the risk is proportional to dose, even at very low doses (<100 mSv), with no threshold. This is the basis for the 5% per Sv coefficient. However, at low doses, the epidemiological evidence is weak, and alternative models exist: (1) the linear-quadratic model (LQ) used in radiotherapy, which assumes a quadratic component at low doses (less risk per unit dose), (2) the hormesis model, suggesting low doses may be beneficial (not accepted by ICRP), and (3) the threshold model, which assumes no effect below a certain dose. The ICRP adopts LNT for protection purposes because it's simple, conservative, and supported by mechanistic studies (DNA damage and repair). Critics argue it overestimates risks at low doses, but without strong evidence for a threshold, the LNT remains the regulatory standard. The calculator uses LNT, but users should be aware of the scientific debate.

Excess risk is the additional risk above the baseline that is attributed to the radiation exposure. In this calculator, Risk = E × 0.05 gives the excess absolute risk (EAR) for cancer mortality—it's the probability that the exposed person will develop a fatal cancer due to radiation. Attributable risk (or attributable fraction) is the proportion of the total risk in the exposed group that is due to the exposure, calculated as (excess risk) / (baseline + excess risk). For a small dose (like 1 mSv), the excess risk is ~0.005%, while baseline risk is ~25%, so the attributable fraction is about 0.02%—almost all of the risk is from natural causes. The calculator does not output attributable risk, but it's an important concept for risk communication: even with a large dose of 100 mSv (0.5% excess risk), most of the cancer risk in that person remains due to non-radiation factors.

The ICRP's 5% per Sv coefficient is for total effective dose, regardless of dose rate, assuming the LNT model and that risks are additive. This means a 10 mSv acute dose from a CT scan is treated as having the same risk as a 10 mSv chronic dose accumulated over a year from background radiation, according to the LNT model. However, the scientific evidence suggests that at very low dose rates, the risk might be lower (the 'dose and dose-rate effectiveness factor' or DDREF). The ICRP uses a DDREF of 2 for solid cancers, meaning that low-dose, low-dose-rate exposures (like background) are considered to have half the risk per Sv compared to acute exposures (like a CT scan). The calculator uses the simple 5% coefficient without DDREF, as it's a conservative screening tool, but for more accurate assessments, you might apply a correction factor based on the dose rate. For occupational and public exposures, the DDREF is often ignored for simplicity.

The heritable risk coefficient of 0.1% per Sv applies to 'severe' heritable diseases that are clinically significant, impairing quality of life or reducing life expectancy. This includes diseases like cystic fibrosis, muscular dystrophy, Huntington's disease, and severe congenital malformations. It does not include mild effects like minor congenital anomalies or early-onset cataracts, which are less well-documented. The coefficient is derived from the 'doubling dose' concept: the radiation dose required to double the spontaneous mutation rate. For chronic radiation, the doubling dose is estimated at ~1 Sv, so a dose of 1 Sv would increase the mutation rate by 100%, but since the background heritable disease incidence is ~5%, a 1 Sv dose adds only 0.5% risk—which is where the 0.1% per 1 mSv comes from? Wait, careful: 0.1% per Sv means a 1 Sv dose adds 0.001 absolute risk (0.1%). For a 20 mSv occupational dose, the heritable risk is 0.002% (2e-5), which is about 50 times smaller than the cancer risk, hence it's often considered negligible in practical radiation protection.

The ICRP's 5% per Sv for cancer mortality is the most widely used international standard. The US EPA uses a similar coefficient of about 5.5% per Sv (for all cancers, including non-fatal, resulting from their own analysis). UNSCEAR typically reports a range of 4-6% per Sv, depending on the population and age distribution. The BEIR VII report (National Academies, 2006) gives a lifetime cancer mortality risk of about 4.1% per Sv for the US population, with an incidence risk of 10.5% per Sv. The differences stem from different models, baseline cancer rates, and assumptions about DDREF. The calculator uses the ICRP value of 5% for simplicity, which is widely accepted for radiation protection purposes. For a specific application (e.g., regulatory compliance in the US), you might substitute 5.5% based on EPA guidance, but the order of magnitude is the same.

Yes, under the LNT model, the risk is strictly linear: 100 mSv (0.1 Sv) gives 0.1 × 0.05 = 0.005 = 0.5% excess fatal cancer risk. A 10 mSv dose gives 0.05%, and 1 mSv gives 0.005%. This linearity extends down to zero dose by definition of the LNT model. However, the statistical uncertainty in the epidemiological data is huge at these low doses; the confidence intervals for risk at 1 mSv may span from near zero to several times the central estimate. The ICRP and most regulators accept the linear extrapolation as a simplifying and conservative assumption for protection purposes, not as an accurate estimate of individual risk. At doses below 10 mSv, the 'risk' is so small that it's essentially unmeasurable in epidemiological studies, and the model may overestimate the actual risk.

Excess risk (or absolute excess risk) is the additional probability of an outcome (e.g., cancer) in an exposed population compared to an unexposed population, expressed as an absolute difference. The calculator provides the excess absolute risk (EAR): Risk = E × 0.05. Relative risk (RR) is the ratio of risk in exposed to unexposed (e.g., RR = (baseline + excess)/baseline). For a small dose, RR is close to 1. Absolute risk is the total probability of the outcome (baseline + excess). The ICRP uses excess risk because it's directly additive across different sources of exposure, making it suitable for summing risks from multiple sources. In risk communication, relative risk is often easier for the public to understand ('your risk increases by X%'), but for radiation protection calculations, excess risk is the standard metric.

The effective dose (E) in Sv already incorporates the organ-specific absorbed doses weighted by tissue weighting factors (w_T) that reflect the different radiosensitivities of organs (e.g., breast and lung have high w_T, skin and bone surface have low w_T). The 5% per Sv risk coefficient is then applied to the effective dose, assuming that the total risk is the sum of the weighted organ risks. This means the calculator does not need to account for individual organ sensitivities separately; the averaging is already done in the effective dose. For a specific organ (e.g., thyroid), the risk per Sv for that organ would be higher, but the effective dose is a whole-body equivalent designed for comparing different exposure scenarios. This is why the calculator is intended for population-level screening, not for detailed organ-specific risk estimation.