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Methodology & Sources

All formulas, assumptions, lookup tables, caveats, and source references used in SunSafe Timer. This is an educational tool — not medical advice.

Educational estimates only. All numbers produced by SunSafe Timer are rough approximations based on population-level reference values. Individual biology, cloud cover, altitude, sunscreen use, and many other factors substantially alter real-world UV exposure. Do not use these estimates to make medical decisions. Consult a dermatologist or physician for personalized advice.

Unit Conversions

These are the fundamental unit relationships that underpin all SunSafe calculations.

1 UV Index unit = 25 mW/m² = 0.025 W/m² (erythemally weighted irradiance — WHO definition) 1 SED = 100 J/m² (Standard Erythemal Dose — ICNIRP definition) SED per minute = (irradiance × time) / 1 SED = (0.025 W/m² × UVI × 60 s) / 100 J/SED = 0.015 × UV Index Burn time (min) = MED_SED / (0.015 × UV Index)

Source: WHO Global Solar UV Index: A Practical Guide (2002), Section 3.2 — UV Index definition. ICNIRP UV radiation guidelines (2010) — SED definition.

Sunburn Model

The burn threshold is expressed as a MED (Minimal Erythemal Dose) — the minimum UV dose required to produce the first detectable redness (erythema) in untanned skin, measured 24 hours after exposure under standard conditions.

Step 1: dose_sed = minutes × (0.015 × UV_Index) Step 2: burn_threshold_reached when dose_sed ≥ MED_SED Step 3: burn_time_minutes = MED_SED / (0.015 × UV_Index)

MED Lookup Table — Fitzpatrick Skin Type

MED values represent the dose for untanned, unprotected skin in a standard UV field. Tanning, sunscreen, or prior UV exposure all modify the effective MED.

Type Description Typical Reaction MED (SED) MED (J/m²)
I Very fair, white skin; red/blonde hair; blue/green eyes; freckles Always burns, never tans 2.0 200
II Fair, white skin; light hair; blue/hazel eyes Usually burns, tans minimally 3.0 300
III Medium/olive skin; brown hair and eyes Sometimes burns, tans uniformly 4.5 450
IV Olive/light brown skin; dark hair and eyes Rarely burns, tans well 6.0 600
V Brown skin; dark brown/black hair; dark eyes Very rarely burns, tans very easily 8.0 800
VI Dark brown/black skin; black hair; dark eyes Never burns, deeply pigmented 10.0 1000

Sources: WHO UV Index Practical Guide (2002); Fitzpatrick TB (1988) J Am Acad Dermatol; IARC Monographs Vol 100D (2012); typical population MED ranges — individual values vary widely.

Vitamin D Estimation Model

The vitamin D estimate is based on Holick's rule, a rough order-of-magnitude educational estimate:

"Approximately 1,000 IU of vitamin D₃ is produced when 1/4 of the body surface area is exposed to approximately 1/4 MED of UVB radiation."
— Holick MF, Am J Clin Nutr (2004)
Step 1: dose_sed = minutes × (0.015 × UV_Index) Step 2: dose_fraction_med = dose_sed / MED_SED Step 3: vitamin_d_iu = 1000 × (dose_fraction_med / 0.25) × (exposed_bsa_fraction / 0.25) Cap: Max 15,000 IU per session (single-session photosynthesis plateau)

Reliability Flags

Condition Flag Reason
Dose < 0.5 MED Reliable range Linear relationship between dose and vitamin D production holds
Dose 0.5–1.0 MED Less reliable Tanning/pigmentation begins; photoproduction efficiency decreases
Dose ≥ 1.0 MED Unreliable + burn warning Burn threshold reached; photoproduction does not increase further; vitamin D is degraded by further UV
UV Index < 3 Low UVI note Mainly UVA at low UV levels; UVA (315–400 nm) does NOT produce vitamin D — only UVB (280–315 nm) does

Body Surface Area Presets

These presets are approximate anatomical estimates for average adults. Individual anatomy, body habitus, clothing cut, and exact posture all affect actual BSA.

PresetBSA FractionApproximate % of Total
Face & hands only0.05~5%
T-shirt + shorts0.35~35%
Tank top + shorts0.45~45%
One-piece swimsuit0.60~60%
Bikini / swim trunks0.80~80%
Nearly full body0.90~90%

Rule of Nines (Advanced Mode)

The Rule of Nines (Wallace Rule) divides total BSA into 11% increments for clinical burn estimation. SunSafe uses a simplified version for educational purposes.

Body RegionBSA Fraction
Head & neck0.09 (9%)
Chest (front)0.09
Abdomen (front)0.09
Upper back0.09
Lower back0.09
Right arm0.09
Left arm0.09
Right thigh0.095
Left thigh0.095
Right lower leg0.07
Left lower leg0.07
Genitalia0.01 — not included in MVP

Assumptions, Caveats, and Limitations

  • Untanned, unprotected skin: All MED values assume no prior tan and no sunscreen. Sunscreen with SPF 30 reduces effective UV dose by ~97%.
  • Clear-sky UVI is an overestimate: Cloud cover, air pollution, and aerosols reduce actual UVI below the clear-sky value by 10–90%.
  • Altitude effect: UV increases ~10–12% per 1,000 m of altitude. High-altitude users will burn faster than calculated.
  • Reflection surfaces: Snow reflects 80–85% of UV; water ~10–30%; sand ~10–15%. Near these surfaces, effective UVI is substantially higher.
  • Vitamin D UVB dependency: Only UVB (280–315 nm) produces vitamin D. In the early morning and late afternoon, the solar zenith angle filters out most UVB — the "shadow rule" (your shadow longer than your height) is a simple proxy for inadequate UVB.
  • Season and latitude: At latitudes above ~35°N or S, UVB is insufficient for vitamin D synthesis from November to March (varies by location).
  • Age: Older adults produce vitamin D less efficiently — an 80-year-old's skin produces ~4× less than a 20-year-old's at the same UV dose.
  • Glass windows: Standard glass blocks essentially all UVB. Driving or sitting by a window does not produce vitamin D.
  • Medications: Certain photosensitizing medications (tetracyclines, fluoroquinolones, thiazides, retinoids, NSAIDs, and others) significantly increase burn risk. Consult your physician or pharmacist.
  • Prior exposure: Accumulated tanning shifts the effective MED upward over days to weeks. A freshly arrived tourist burns faster than a local who has been sun-exposed for weeks.
  • Holick's formula is a rough estimate: Real photosynthesis of pre-vitamin D₃ is a complex photochemical process. The linear approximation used here deviates substantially at high doses and in deeply pigmented skin.
  • Temperature is context only: UV Index, not temperature, determines sunburn risk. A cool overcast day can have significant UV; a hot day with high aerosols can have lower effective UV than the index suggests.

References

  1. World Health Organization (2002). Global Solar UV Index: A Practical Guide. WHO/SDE/OEH/02.2. Geneva: World Health Organization. who.int
  2. International Commission on Non-Ionizing Radiation Protection (ICNIRP) (2010). ICNIRP Statement — Limits of Exposure to Ultraviolet Radiation of Wavelengths 180–400 nm. Health Physics, 87(2), 171–186. icnirp.org
  3. Holick MF (2004). Sunlight and vitamin D for bone health and prevention of autoimmune diseases, cancers, and cardiovascular disease. Am J Clin Nutr, 80(6 Suppl), 1678S–1688S. PMID 15585788. PubMed
  4. Webb AR, Engelsen O (2006). Calculated ultraviolet exposure levels for a healthy vitamin D status. Photochem Photobiol, 82(6), 1697–1703. PMID 16999790. PubMed
  5. Fitzpatrick TB (1988). The validity and practicality of sun-reactive skin types I through VI. Arch Dermatol, 124(6), 869–871. PMID 3377516. PubMed
  6. Lucas R, McMichael T, Smith W, Armstrong B (2006). Solar ultraviolet radiation. Global burden of disease from solar ultraviolet radiation. Environmental Burden of Disease Series No. 13. WHO. Geneva. who.int
  7. IARC Working Group on the Evaluation of Carcinogenic Risks to Humans (2012). Solar and Ultraviolet Radiation. IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, Vol 100D. IARC
  8. Bouillon R et al. (2022). Vitamin D and human health: lessons from vitamin D receptor null mice. Endocr Rev, 29(6), 726–776. PMID 19196837. PubMed
  9. Open-Meteo (2023). Open-Meteo Weather API Documentation. open-meteo.com
  10. Wallace AB (1951). The exposure treatment of burns. Lancet, 261(6653), 501–504. (Rule of Nines original description.) PMID 14805108.