Calculate TSH from Free T4 or Total T3, or check a TSH result against adult, age-adjusted, pregnancy, and pediatric reference ranges.

Required: your TSH result.

mIU/L and uIU/mL are numerically the same unit.

+ Add Free T4 for pattern and TSH Index

Related Calculators

TSH Formula

The following formulas can be used to estimate the TSH (thyroid-stimulating hormone) level from FT4 or T3 using simplified log-linear relationships.

Equation 1 – FT4 model (Benhadi et al., 2010)
log10(TSH) = 1.50 − 0.059 × FT4(pmol L−1)
⇒ TSH (mIU L−1) = 10[1.50 − 0.059 × (FT4(ng/dL) × 12.87)]

Equation 2 – T3 model (educational approximation)
log10(TSH) = 0.790 − 0.245 × T3(nmol L−1)
⇒ TSH (mIU L−1) = 10[0.790 − 0.245 × (T3(ng/dL) × 0.01536)]

*These empiric formulas describe an average negative-feedback curve and are not a substitute for laboratory measurement or clinical judgment. The FT4 relationship is generally more clinically useful than a T3-only estimate.*

Variables:

  • TSH is the thyroid-stimulating hormone level (mIU/L).
  • FT4 is the free thyroxine level (ng/dL; sometimes reported as pmol/L).
  • T3 is typically the total triiodothyronine level (ng/dL; sometimes reported as nmol/L).

What is TSH?

TSH, or thyroid-stimulating hormone, is a hormone produced by the pituitary gland in the brain. It plays a crucial role in regulating the function of the thyroid gland, which is responsible for controlling the body’s metabolism. A TSH test is often used to diagnose thyroid disorders, such as hypothyroidism or hyperthyroidism, by measuring the level of TSH in the blood.

How to Calculate TSH (Estimate)?

The following steps outline how to estimate TSH using the equations above:

  1. Choose which equation to use: the FT4-based equation (preferred) or the T3-based approximation.
  2. If using FT4 in ng/dL, convert to pmol/L by multiplying by 12.87.
  3. Compute log10(TSH) using the chosen equation.
  4. Convert back to TSH by calculating TSH = 10log10(TSH).
  5. Check your result with the calculator above (remembering the output is only an estimate).

Example Problem:

Use the following variables as an example problem to test your knowledge:

FT4 (Free T4) = 1.2 ng/dL

T3 (Total T3) = 150 ng/dL

Using the FT4 equation: FT4 = 1.2 × 12.87 = 15.444 pmol/L, so log10(TSH) = 1.50 − 0.059 × 15.444 = 0.5888 and TSH ≈ 100.5888 = 3.882 mIU/L (approx.).