Radiation Distance Calculator
Radiation intensity falls with the square of the distance: step twice as far from a point source and the intensity drops to a quarter. This calculator uses that inverse square law four ways, finding the safe distance for a target exposure level, the intensity at a new distance, the source strength behind a measurement, or the distance a measurement must have been taken from. It is a planning aid; real radiation work still needs calibrated instruments and qualified supervision.
Every input must be a positive number; blank, zero and negative entries are rejected with a prompt. Results in the Intensity and Source strength modes are plain numbers in whatever unit you entered, and distance results are labelled meters, so keep your units consistent within a mode.
Quick Answer
If a meter reads 100 µSv/h at 2 metres from a source and your target is 25 µSv/h, the safe distance is 4.00 meters: D₂ = 2 × √(100 ÷ 25) = 2 × 2. That is a distance factor of 2.00, because doubling the distance quarters the intensity.
- Quick Answer
- How to use the radiation distance calculator
- The inverse square law, solved four ways
- Worked examples for all four modes
- How intensity scales with distance
- Why distance is the strongest of the three protections
- Assumptions and limits of the point-source model
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
How to use the radiation distance calculator
Each of the four modes solves the same equation for a different unknown. Pick the mode named after the number you need; the worked example for that mode is pre-filled.
- Safe distance: enter the measured intensity I₁, the distance D₁ where it was measured, and your target intensity I₂. The tool returns the required distance plus the distance factor, how many times farther than D₁ you must stand.
- Intensity: enter a known intensity I₁ at D₁ and a new distance D₂. The tool returns the intensity at D₂ as a plain number in your unit.
- Source strength: enter a measured intensity I₂ at D₂ and a reference distance D₁. The tool works back to the intensity at D₁.
- Measurement distance: enter the source intensity I₁, a measured intensity I₂, and the distance D₂ of that measurement. The tool recovers the original distance D₁ the source intensity refers to.
Every field must be positive. Blank, zero, negative or non-numeric entries are rejected with a prompt naming the field, for example "Please enter a valid positive measured intensity." Results stay hidden until you click Calculate in that mode.
The inverse square law, solved four ways
All four modes are rearrangements of one identity: for a point source, intensity times distance squared is constant, I₁ × D₁² = I₂ × D₂². If you only ever need the general law without the radiation framing, the inverse square law calculator solves the same four rearrangements for light, sound and other quantities.
Intensity at new distance: I₂ = I₁ × (D₁ ÷ D₂)²
Source intensity: I₁ = I₂ × (D₂ ÷ D₁)²
Original distance: D₁ = D₂ × √(I₂ ÷ I₁)
The square root appears in the distance modes because distance enters the law squared. Halving an intensity therefore does not need double the distance; it needs √2 ≈ 1.41 times the distance. The fraction form, I₂/I₁ = (D₁/D₂)², is the version university radiation safety courses teach, for example in the Open Oregon radiation safety worksheet built around the NRC material.
Worked examples for all four modes
Each mode ships pre-filled with its own example, so you can reproduce every row below by switching tabs and clicking Calculate.
| Mode | Inputs | Working | Result |
|---|---|---|---|
| Safe distance | 100 µSv/h at 2 m, target 25 µSv/h | 2 × √(100 ÷ 25) = 2 × 2 | 4.00 meters, factor 2.00 |
| Intensity | 400 W/m² at 2 m, new distance 5 m | 400 × (2 ÷ 5)² = 400 × 0.16 | 64.00 (W/m²) |
| Source strength | 64 W/m² measured at 5 m, reference 2 m | 64 × (5 ÷ 2)² = 64 × 6.25 | 400.00 (W/m²) |
| Measurement distance | Source 100, measured 25 at 4 m | 4 × √(25 ÷ 100) = 4 × 0.5 | 2.00 meters |
Two edge cases worth knowing: if your target intensity in Safe distance mode is higher than the measured intensity, the tool happily returns a factor below 1 (25 measured at 4 m with a target of 100 gives 2.00 meters, factor 0.50), which simply means you could stand closer. And moving closer in Intensity mode raises the reading just as fast: 25 at 4 m becomes 100.00 at 2 m.
How intensity scales with distance
The whole law fits in one pattern: multiply the distance by a factor and the intensity divides by that factor squared. These are the multipliers worth memorising for barrier and boundary work.
| Distance multiplier | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| Intensity remaining | 100% | 25% | 11.11% | 6.25% | 4% | 1% |
Why distance is the strongest of the three protections
Radiation protection rests on time, distance and shielding, and distance is the only one of the three that pays out quadratically. Halving your time near a source halves your dose; doubling your distance quarters the dose rate itself. That is why the OSHA guidance on controlling ionizing radiation exposure tells workers to maximise distance first: for gamma rays and X-rays the dose rate follows the inverse square law, so a factor of 2 in distance is a factor of 4 in dose rate.
Distance is also the cheapest control to apply and the easiest to verify. A barrier position can be measured with a tape, a survey meter confirms the result, and nobody has to wear or maintain anything. Shielding still matters when you cannot step back, and time limits still matter for the dose you accumulate while you are there, but the safe-distance mode above is where a sensible work plan starts. Do not confuse this tool with the radio distance calculator, which works out line-of-sight range from antenna heights for communications links, a completely different distance problem.
Assumptions and limits of the point-source model
The inverse square law is exact geometry and approximate physics. Four limits decide how far to trust any number it gives you.
- Point source in open space. The law assumes radiation streaming out evenly from a point with nothing in the way. Very close to the source, or near an extended source such as a contaminated floor, the geometry breaks down and real intensities fall off more slowly than the law predicts.
- No shielding, scatter or absorption. Walls, air and the source's own housing all change the field. Scatter inside a room can add dose the law never counts, so treat every result as a planning figure to verify with a calibrated survey instrument, not as a clearance.
- Units are your responsibility. The tool converts nothing. Intensity modes return a bare number in whatever unit you entered (enter µSv/h, read µSv/h), and the distance answers are labelled "meters" even if you worked in feet. Mixing units inside one mode gives a confident, wrong answer.
- The target limit is yours to supply. Occupational limits, public limits and medical reference levels are set by regulators and differ by country and task. The calculator applies the limit you type in; it does not know or judge it.
What competing calculators miss
Most inverse-square tools were built for lighting or homework, and it shows when you bring them a radiation problem:
- Relative-factor-only tools (Brave Calculator's radiation distance page): its stated formula, D = √(I₁/I₂), returns only the relative distance factor. Without the measurement distance multiplied back in, there is no absolute answer to tape out on the floor.
- Generic inverse-square solvers (CalculatorsHub, Firgelli): all four rearrangements are there, but framed for lumens, lux and W/m² lighting work, with no safe-limit concept, no radiation units and nothing about the point-source assumptions.
- Shielding-first tools (Firgelli's radiation shielding calculator): genuinely deeper, combining source activity, gamma constants and barrier transmission, but it answers a different question, what a shielded boundary distance is, and buries the simple unshielded case a first estimate needs.
- The gap this page fills: all four rearrangements in one radiation-specific tool, a safe-distance mode that returns an absolute distance and its factor, the assumptions stated on the page, and copy and share on every mode.
Frequently asked questions
Radiation intensity from a point source decreases with the square of the distance: I₁ × D₁² = I₂ × D₂². Double the distance and you get one quarter of the intensity; triple it and you get one ninth. All four modes of this calculator are rearrangements of that one equation.
Measure or estimate the intensity I₁ at a known distance D₁, choose your target intensity I₂, and use the safe-distance mode: D₂ = D₁ × √(I₁ ÷ I₂). A reading of 100 µSv/h at 2 m with a 25 µSv/h target gives 4.00 meters. Then add a margin and verify with a calibrated instrument.
Any consistent units: µSv/h or mSv/h for intensity as long as I₁ and I₂ match, meters or feet for distance as long as D₁ and D₂ match. The tool does not convert units, the intensity answers come back as plain numbers in your unit, and distance answers are labelled meters regardless.
It describes the geometric spreading of radiation from a point source, and it is most directly applicable to gamma rays and X-rays. Alpha and beta particles also lose energy as they travel through air, so their intensity falls off even faster than the law predicts.
The radiation spreads over the surface of an expanding sphere, and a sphere's surface area grows with the square of its radius. Twice the radius means four times the area, so each unit of area receives one quarter of the radiation.
Yes. The same law governs light intensity, sound intensity and other point-source quantities: enter a known intensity at a known distance and solve for the value or distance you need, keeping your units consistent. The radiation labels are framing; the math is the general inverse square law.
There is no single number this tool can give you. Occupational limits, public limits and medical reference levels are set by regulators and differ by country, task and who is exposed. Take the target intensity from the standard that applies to your work and enter it as I₂; the calculator applies your limit, it does not set one.
Yes. Shielding attenuates radiation on top of the distance effect, roughly exponentially with thickness, so a shielded position can be closer than the distance-only answer. This calculator models distance alone; treat its result as the unshielded, conservative starting point and account for shielding separately.
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References
- U.S. Occupational Safety and Health Administration. Ionizing Radiation: Control and Prevention (ALARA programs and the time, distance and shielding controls; inverse square law for gamma and X-ray dose rates). Accessed October 24, 2026.
- Open Oregon Educational Resources. Radiation Safety: ALARA and the Inverse Square Law Worksheet (NRC-based teaching material solving the inverse square law for safe distances and intensities). Accessed October 24, 2026.
- The Catholic University of America, Environmental Health and Safety. Radiation Safety Manual, Section 9.3: Rules for Control and Monitoring (occupational dose limits under 10 CFR 20 and time, distance and shielding practice). Accessed October 24, 2026.
- CASRAI. ALARA: Time, Distance and Shielding (ALARA as a regulatory requirement under 10 CFR 20.1101, and why distance outperforms time for dose reduction). Accessed October 24, 2026.
- Versant Physics. ALARA: The Gold Standard of Radiation Protection (medical physics practice for time, distance and shielding in clinical settings). Accessed October 24, 2026.
- U.S. Nuclear Regulatory Commission. Backgrounder on Biological Effects of Radiation (health effects background behind the dose limits the target intensity is drawn from). Accessed October 24, 2026.