A calibration curve plotting absorbance versus concentration following Beer-Lambert law (A = εlc). Measured calibration standards are shown as scatter points with a linear regression fit line. The regression equation (y = mx + b) and R² value are displayed on the plot. An example unknown sample is marked with dashed lines extending to both axes, demonstrating how the curve is used to determine concentration from a measured absorbance. This plot is fundamental in analytical chemistry for quantitative spectrophotometric analysis.
# anyplot.ai
# calibration-beer-lambert: Beer-Lambert Calibration Curve
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 91/100 | Created: 2026-06-03
using CairoMakie
using Colors
using Random
using Statistics
using Printf
Random.seed!(42)
# Theme tokens (Imprint palette — theme-adaptive chrome)
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73", # 1 — Imprint brand green (always first series)
colorant"#C475FD", # 2 — lavender
colorant"#4467A3", # 3 — blue
colorant"#BD8233", # 4 — ochre
colorant"#AE3030", # 5 — matte red
colorant"#2ABCCD", # 6 — cyan
colorant"#954477", # 7 — rose
colorant"#99B314", # 8 — lime
]
# Data — nitrate colorimetric assay, UV-Vis at 540 nm (environmental water testing)
concentrations = Float64[0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 15.0] # mg/L
true_abs = 0.065 .* concentrations # Beer-Lambert: A = εlc, εl ≈ 0.065 L/mg
noise = randn(length(concentrations)) .* 0.008
absorbance = true_abs .+ noise
absorbance[1] = max(0.0, absorbance[1]) # blank must be non-negative
# Linear regression (ordinary least squares)
n = length(concentrations)
x_mean = mean(concentrations)
y_mean = mean(absorbance)
sxx = sum((concentrations .- x_mean) .^ 2)
sxy = sum((concentrations .- x_mean) .* (absorbance .- y_mean))
slope = sxy / sxx
intercept = y_mean - slope * x_mean
# Goodness of fit
y_pred_cal = slope .* concentrations .+ intercept
ss_res = sum((absorbance .- y_pred_cal) .^ 2)
ss_tot = sum((absorbance .- y_mean) .^ 2)
r_squared = 1.0 - ss_res / ss_tot
# Regression line and 95% prediction interval
x_fit = collect(range(0.0, 16.5, length=300))
y_fit = slope .* x_fit .+ intercept
s2 = ss_res / (n - 2) # mean squared error
se_pred = sqrt.(s2 .* (1.0 ./ n .+ (x_fit .- x_mean) .^ 2 ./ sxx))
t_crit = 2.447 # t(0.025, df=6) for 95% prediction interval
y_upper = y_fit .+ t_crit .* se_pred
y_lower = y_fit .- t_crit .* se_pred
# Unknown sample: determine concentration from measured absorbance
unknown_abs = 0.520
unknown_conc = (unknown_abs - intercept) / slope
# Annotation string
eq_str = @sprintf("y = %.4fx %+.4f\nR² = %.4f", slope, intercept, r_squared)
# Plot
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "calibration-beer-lambert · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Concentration (mg/L)",
ylabel = "Absorbance",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
xminorgridvisible = false,
yminorgridvisible = false,
)
# 95% prediction interval band
band!(ax, x_fit, y_lower, y_upper;
color = (IMPRINT_PALETTE[1], 0.15),
label = "95% Prediction interval")
# Regression line
lines!(ax, x_fit, y_fit;
color = IMPRINT_PALETTE[1],
linewidth = 2.5,
label = "Linear fit")
# Calibration standard points
scatter!(ax, concentrations, absorbance;
color = IMPRINT_PALETTE[1],
markersize = 14,
strokecolor = PAGE_BG,
strokewidth = 1,
label = "Calibration standards",
)
# Dashed guide lines for unknown sample determination (no legend entry)
lines!(ax, [0.0, unknown_conc], [unknown_abs, unknown_abs];
color = IMPRINT_PALETTE[3],
linewidth = 1.5,
linestyle = :dash,
)
lines!(ax, [unknown_conc, unknown_conc], [0.0, unknown_abs];
color = IMPRINT_PALETTE[3],
linewidth = 1.5,
linestyle = :dash,
)
# Unknown sample marker
scatter!(ax, [unknown_conc], [unknown_abs];
color = IMPRINT_PALETTE[3],
markersize = 16,
marker = :diamond,
strokecolor = PAGE_BG,
strokewidth = 1,
label = "Unknown sample (A = 0.520)",
)
# Regression equation and R² annotation (lower-right area, data coordinates)
text!(ax, 15.8, 0.04;
text = eq_str,
align = (:right, :bottom),
color = INK_MUTED,
fontsize = 15,
)
xlims!(ax, -0.5, 17.0)
ylims!(ax, -0.05, 1.15)
# Legend — identifies all four visual elements for unfamiliar readers
axislegend(ax;
position = :lt,
labelcolor = INK,
labelsize = 12,
framecolor = INK_SOFT,
backgroundcolor = ELEVATED_BG,
framevisible = true,
)
# Save
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/calibration-beer-lambert/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "calibration-beer-lambert",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/calibration-beer-lambert/julia/makie",
"hub": "https://anyplot.ai/calibration-beer-lambert",
"code_json": "https://api.anyplot.ai/specs/calibration-beer-lambert/makie/code",
"spec_json": "https://api.anyplot.ai/specs/calibration-beer-lambert",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/calibration-beer-lambert/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/calibration-beer-lambert/julia/makie/plot-dark.png",
"quality_score": 91.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Beer-Lambert Calibration Curve on anyplot.ai.