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Radiation shielding half-value layer calculator

A shield three half-value layers thick, 7.5 against a half-value layer of 2.5 in the same unit, cuts an intensity of 1000 to 125: a transmission of 0.125 and 87.5 % attenuation. Free in your browser.

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Worked example

If you enter

Initial intensity: 1,000
Shield thickness: 7.5
Half value layer: 2.5

You get

Transmitted intensity: 125
Transmission fraction: 0.125
Attenuation percent: 87.5
Half value layers: 3

This radiation shielding half-value-layer calculator estimates the intensity that remains after radiation passes through a specified shield thickness. Enter the unshielded intensity, the total thickness, and the material's half-value-layer thickness in matching length units. The calculator applies exponential attenuation, reports how many half-value layers the shield represents, and returns both the transmitted fraction and attenuation percentage. It is intended for transparent engineering estimates when an appropriate HVL is already known.

Set up the three quantities consistently

Start with the radiation intensity measured or specified before the shield. The calculator preserves that intensity unit, so an input in counts per minute, dose rate, air kerma rate, or another intensity-like unit produces transmitted intensity in the same unit. Next, provide the total shield thickness and the half-value-layer thickness for the relevant radiation energy and material.

Those two lengths may be entered in millimeters, centimeters, inches, or another unit, but they must use the same unit because the calculation depends on their ratio. A half-value layer is the thickness that reduces the primary intensity to one half under the conditions for which the HVL was determined. Do not substitute density, mass thickness, or a value for a different beam quality without first making the required conversion.

The model requires a strictly positive HVL. A zero or negative value has no physical meaning in this formula and is returned as an input error instead of allowing an undefined division or misleading result.

Understand the attenuation calculation

The calculation uses I = I0 × 2<sup>−x/HVL</sup>, where I0 is initial intensity, x is shield thickness, and HVL is half-value-layer thickness. Dividing thickness by HVL gives the number of half-value layers in the shield. One layer leaves one half of the original intensity, two layers leave one quarter, and three layers leave one eighth.

Fractional layer counts work in exactly the same exponential relationship; a shield does not need to contain a whole number of HVLs. The returned transmission fraction is the multiplier applied to initial intensity. Attenuation percentage is one minus that fraction, expressed as a percentage.

For example, a transmission fraction of 0.125 corresponds to 87.5 percent attenuation. A zero shield thickness is valid and returns the initial intensity unchanged. A zero initial intensity is also valid and remains zero, although the transmission fraction still describes what the shield would transmit.

Outputs are rounded only to stabilize representation, while the calculation uses JavaScript floating-point arithmetic throughout.

Use the result within the model's limits

Half-value-layer attenuation is useful for quick comparisons, preliminary shielding estimates, classroom work, and checking repeated halving calculations. It is not a complete radiation transport model. Real installations may require energy-dependent attenuation coefficients, broad-beam geometry, buildup factors, secondary radiation, scattering, shield penetrations, source geometry, material composition, occupancy, distance, and regulatory design margins.

The HVL itself depends on the radiation type, energy spectrum, material, and measurement geometry, so obtain it from a suitable measured or authoritative source for the exact application. This calculator assumes the supplied HVL remains constant through the full shield, an approximation that may be inappropriate when beam hardening changes the spectrum as radiation penetrates matter. Treat the result as transmitted primary intensity under the stated exponential model, not as an automatic claim of safety or compliance.

For medical, industrial, nuclear, or occupational protection decisions, have the inputs, assumptions, and resulting shield design reviewed by a qualified radiation-protection professional using the standards and rules applicable to the site.

What you can do with it

Check a repeated-halving calculation

Confirm the remaining intensity after a shield spans one, two, three, or a fractional number of half-value layers.

Compare candidate thicknesses

Evaluate how changing shield thickness affects primary-beam transmission when the same appropriate HVL applies.

Document a preliminary estimate

Record the formula, layer count, transmission fraction, attenuation percentage, and transmitted intensity for an engineering note.

FAQ

What is a half-value layer?

It is the thickness of a specified material that reduces the primary radiation intensity to one half under specified beam and measurement conditions.

Must shield thickness and HVL use the same unit?

Yes. Their ratio must be dimensionless. You may use any length unit, provided both values use that same unit.

Does the calculator include radiation buildup or scattering?

No. It applies the simple exponential HVL model to primary intensity and does not calculate buildup, scattering, leakage, or secondary radiation.

Does the shield need a whole number of half-value layers?

No. Fractional layer counts follow the same exponential rule, so any thickness works. One layer leaves half the intensity, two leave a quarter and three leave an eighth, with every value in between handled the same way.

Which half-value layer should I enter?

The one measured for your shielding material and for the energy of the radiation you are dealing with. Do not substitute density, mass thickness or a value for a different beam quality without converting it first.

Related tools

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/earth/shielding-half-value-layer

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/earth/shielding-half-value-layer \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"initial_intensity":1000,"shield_thickness":7.5,"half_value_layer":2.5}'

const res = await fetch("https://api.kit.forhosting.com/earth/shielding-half-value-layer", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "initial_intensity": 1000,
    "shield_thickness": 7.5,
    "half_value_layer": 2.5
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/earth/shielding-half-value-layer",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "initial_intensity": 1000,
    "shield_thickness": 7.5,
    "half_value_layer": 2.5
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/shielding-half-value-layer", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"initial_intensity":1000,"shield_thickness":7.5,"half_value_layer":2.5}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"initial_intensity":1000,"shield_thickness":7.5,"half_value_layer":2.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/shielding-half-value-layer", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "initial_intensity": 1000,
  "shield_thickness": 7.5,
  "half_value_layer": 2.5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "earth.shielding_half_value_layer",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Technical questions

What happens if the half-value layer is zero or negative?

The request returns an invalid_input error because the formula requires a strictly positive half-value-layer thickness.

What does an API request cost?

Each API request costs $0.002. The browser calculator can run the same deterministic calculation without a network call.

Read the full KIT documentation →

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