Error Propagation Calculator
Multiplying 100 ± 1 by 20 ± 0.4 gives 2000 ± 60: the relative errors 1 % and 2 % add to 3 %.
2000
- Absolute error ±Δy
- 60
- Relative error Δy/|y|
- 3 %
Step-by-step solution
- Δy/y = ΔA/A + ΔB/B = 1 % + 2 % = 3 %
- y = 2000 ± 60
Error Propagation Formula
Sums: ΔA + ΔB; products: ΔA/A + ΔB/B
powers: Δy/y = |n| ΔA/A; statistical errors combine as √(Σ squares)
Worked Example
A = 100 ± 1 and B = 20 ± 0.4 multiplied, limiting errors:
- Δy/y = ΔA/A + ΔB/B = 1 % + 2 % = 3 %
- y = 2000 ± 60
Relative error Δy/|y|: 3 %
GATE tip
For P = I²R, the relative error is 2(ΔI/I) + ΔR/R. Powers multiply their relative error: this single rule handles most GATE measurement-error questions.
More Measurements Calculators
-
Wheatstone Bridge Calculator
Rₓ = R₂R₃ / R₁ at balance
Vₒᵤₜ = V_s [R₂/(R₁ + R₂) − Rₓ/(R₃ + Rₓ)]
Example: A bridge with equal 1 kΩ ratio arms balanced with R₃ = 470 Ω: Unknown resistance Rₓ = 470 Ω.
-
Ammeter Shunt Calculator
R_sh = I_m R_m / (I − I_m), R_s = V/I_m − R_m
multiplying power m = I/I_m, so R_sh = R_m/(m − 1)
Example: A 1 mA, 100 Ω meter extended to read 1 A: Shunt resistance R_sh = 0.1001 Ω.
Frequently asked questions
Limiting or statistical?
Limiting (guaranteed) error adds the worst cases and suits instrument specifications; the root-sum-square suits independent random errors and gives a smaller, more realistic figure.
Why do subtractions magnify errors?
Absolute errors add while the result shrinks: 100 ± 1 minus 98 ± 1 is 2 ± 2, a 100 % error.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Error Propagation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/error-propagation-calculator/
IEEE
Scientific Converters, "Error Propagation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/error-propagation-calculator/