Radiation Equivalent Dose (Sv) Calculator

What is Radiation Dosimetry & Biological Effects?

Not all radiation is equally dangerous. A gray (Gy) measures the raw energy deposited in tissue, but alpha particles cause roughly 20 times more biological damage per gray than gamma rays because they are heavy, slow, and ionize every molecule along a short, dense track. The equivalent dose in sieverts (Sv) corrects for this by multiplying the absorbed dose by a radiation weighting factor (wR). This gives a single number that reflects actual biological risk regardless of radiation type.

Mathematical Foundation

Equivalent Dose

H = D \times w_R

H

= Equivalent dose in sieverts (Sv) — measures biological damage potential

D

= Absorbed dose in grays (Gy) — the raw energy deposited per kilogram of tissue

w_R

= Radiation weighting factor — accounts for the biological effectiveness of different radiation types

Laws & Principles

Weighting Factor (wR): Gamma rays and beta particles have wR = 1. Neutrons range from 5 to 20 depending on energy. Alpha particles have wR = 20. These factors are defined by the ICRP (International Commission on Radiological Protection).
Occupational Dose Limits: The ICRP recommends a maximum occupational effective dose of 20 mSv per year averaged over 5 years, with no single year exceeding 50 mSv. For the general public, the limit is 1 mSv per year above natural background.
Mixed Radiation Fields: When exposed to multiple radiation types simultaneously, calculate the equivalent dose for each type separately and sum them. The total equivalent dose is H_total = sum of (D_i x wR_i) for all radiation types.

Step-by-Step Example Walkthrough

" A nuclear medicine technician receives 0.5 mGy from gamma rays and 0.02 mGy from neutrons (10 MeV) during a single procedure. "

1. Gamma equivalent dose: 0.5 mGy x 1 = 0.5 mSv.
2. Neutron equivalent dose: 0.02 mGy x 20 = 0.4 mSv.
3. Total equivalent dose: 0.5 + 0.4 = 0.9 mSv.

Final Result: Total equivalent dose is 0.9 mSv. Despite receiving 25 times less absorbed dose from neutrons, they contribute nearly half the biological risk because of their high weighting factor.

Quick Answer: What is the equivalent dose?

The equivalent dose converts raw absorbed radiation (in grays) into a measure of biological damage potential (in sieverts) by multiplying by the radiation weighting factor. Alpha particles are 20 times more damaging per gray than gamma rays. Enter your absorbed dose and radiation type above to calculate the equivalent dose instantly.

Radiation Exposure Scenarios

Chest CT Scan

Source: X-rays (wR = 1).
Absorbed dose: ~7 mGy average to the chest.
Equivalent dose: 7 mGy × 1 = 7 mSv.
Context: This equals about 2 years of natural background radiation received in a single scan.

Radon Gas Inhalation

Source: Alpha particles from radon-222 decay products (wR = 20).
Absorbed dose: ~0.1 mGy/year to bronchial epithelium.
Equivalent dose: 0.1 × 20 = 2 mSv/year to lung tissue.
Context: Radon is the second leading cause of lung cancer after smoking. The alpha particles' short range means they deposit all their energy in a thin layer of lung cells.

Radiation Weighting Factors (ICRP 103)

Radiation Type	w_R	Why
Gamma rays, X-rays	1	Low LET; sparse ionization along long tracks
Beta particles, electrons	1	Similar ionization density to photons
Protons (>2 MeV)	2	Heavier than electrons; moderate ionization density
Neutrons (energy-dependent)	5 – 20	Indirectly ionizing; produce heavy recoil protons in tissue
Alpha particles, heavy ions	20	High LET; dense ionization causes double-strand DNA breaks

Radiation Safety Guidelines

Do This

✓Sum doses from all radiation types. In a mixed radiation field, calculate H for each type separately and add them. A small alpha dose can dominate the total biological risk even when the gamma dose is much larger in grays.
✓Use ALARA (As Low As Reasonably Achievable). Even below regulatory limits, minimize exposure through time (less time near the source), distance (inverse-square law), and shielding (lead, concrete, water).

Avoid This

✗Don't confuse sieverts with grays. Grays measure energy deposited. Sieverts measure biological damage. For gamma radiation they are numerically equal, but for alpha particles 1 Gy = 20 Sv. Using the wrong unit could underestimate risk by a factor of 20.
✗Don't ignore internal vs external exposure. A gamma source outside the body is less dangerous than alpha-emitting particles inhaled into the lungs. Alpha particles cannot penetrate skin, but once inside they deliver massive localized doses to surrounding tissue.

Frequently Asked Questions

What is the difference between equivalent dose and effective dose?

Equivalent dose (H) applies the radiation weighting factor to account for radiation type. Effective dose (E) goes one step further by applying tissue weighting factors to account for organ sensitivity. For example, bone marrow is more radiosensitive than skin, so the same equivalent dose to marrow produces a higher effective dose than the same dose to skin.

Why are alpha particles so dangerous internally but harmless externally?

Alpha particles are large (2 protons + 2 neutrons) and carry +2 charge. They interact with every atom they pass, depositing all their energy within about 40 micrometers of tissue. Human skin's dead outer layer (stratum corneum) stops them entirely. But if inhaled or ingested, they sit directly against living cells and deliver concentrated ionization that causes double-strand DNA breaks.

How much background radiation does a person receive per year?

The global average is about 2.4 mSv per year from natural sources: cosmic rays (~0.4 mSv), terrestrial gamma (~0.5 mSv), inhaled radon (~1.2 mSv), and ingested radionuclides (~0.3 mSv). Medical imaging adds another 0.5-3 mSv on average in developed countries, making the total roughly 3-6 mSv per year for most people.

What dose level causes acute radiation syndrome?

Acute radiation syndrome (ARS) begins at whole-body doses above approximately 1 Sv (1,000 mSv). At 1-2 Sv, symptoms include nausea and reduced blood cell counts. At 4-5 Sv, the LD50 (lethal dose for 50% of exposed individuals) is reached without medical treatment. Above 8 Sv, survival is unlikely even with intensive care.