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: plotly 6.7.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-06-03
"""
import os
import numpy as np
import plotly.graph_objects as go
# Theme tokens (Imprint palette — see prompts/default-style-guide.md)
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint palette — positions used
BRAND = "#009E73" # calibration standards — position 1, always first series
BLUE = "#4467A3" # regression line — position 3
RED = "#AE3030" # unknown sample — semantic anchor for focal/reference point
# Data - UV-Vis spectrophotometry calibration standards
np.random.seed(42)
concentration = np.array([0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0])
molar_absorptivity = 0.045
absorbance_true = molar_absorptivity * concentration
absorbance = absorbance_true + np.random.normal(0, 0.008, len(concentration))
absorbance[0] = 0.003
# Linear regression
slope, intercept = np.polyfit(concentration, absorbance, 1)
absorbance_pred = slope * concentration + intercept
ss_res = np.sum((absorbance - absorbance_pred) ** 2)
ss_tot = np.sum((absorbance - np.mean(absorbance)) ** 2)
r_squared = 1 - ss_res / ss_tot
# Regression line and 95% prediction interval
conc_fit = np.linspace(-0.5, 15.5, 200)
abs_fit = slope * conc_fit + intercept
n = len(concentration)
conc_mean = np.mean(concentration)
mse = ss_res / (n - 2)
se_pred = np.sqrt(mse * (1 + 1 / n + (conc_fit - conc_mean) ** 2 / np.sum((concentration - conc_mean) ** 2)))
t_crit = 2.447 # t-critical for 95% two-sided, df=6 (pre-computed)
pred_upper = abs_fit + t_crit * se_pred
pred_lower = abs_fit - t_crit * se_pred
# Unknown sample
unknown_absorbance = 0.38
unknown_concentration = (unknown_absorbance - intercept) / slope
# Title — 55 chars, below 67-char baseline → default fontsize applies
title = "calibration-beer-lambert · python · plotly · anyplot.ai"
title_fontsize = round(16 * min(1.0, 67 / len(title)))
# Plot
fig = go.Figure()
# 95% prediction interval band
fig.add_trace(
go.Scatter(
x=np.concatenate([conc_fit, conc_fit[::-1]]),
y=np.concatenate([pred_upper, pred_lower[::-1]]),
fill="toself",
fillcolor="rgba(68,103,163,0.12)",
line={"color": "rgba(0,0,0,0)"},
name="95% Prediction Interval",
showlegend=True,
hoverinfo="skip",
)
)
# Regression line
fig.add_trace(
go.Scatter(
x=conc_fit,
y=abs_fit,
mode="lines",
name=f"Fit: y = {slope:.4f}x + {intercept:.4f}",
line={"color": BLUE, "width": 3},
hovertemplate="Conc: %{x:.2f} mg/L<br>Predicted Abs: %{y:.4f}<extra></extra>",
)
)
# Calibration standards
fig.add_trace(
go.Scatter(
x=concentration,
y=absorbance,
mode="markers",
name="Calibration Standards",
marker={"size": 17, "color": BRAND, "line": {"color": PAGE_BG, "width": 2}, "symbol": "circle"},
hovertemplate="<b>Standard %{pointNumber}</b><br>Concentration: %{x:.1f} mg/L<br>Absorbance: %{y:.4f}<extra></extra>",
)
)
# Unknown sample point
fig.add_trace(
go.Scatter(
x=[unknown_concentration],
y=[unknown_absorbance],
mode="markers",
name=f"Unknown ({unknown_concentration:.1f} mg/L)",
marker={"size": 21, "color": RED, "line": {"color": PAGE_BG, "width": 2}, "symbol": "diamond"},
hovertemplate="<b>Unknown Sample</b><br>Concentration: %{x:.2f} mg/L<br>Absorbance: %{y:.4f}<extra></extra>",
)
)
# Dashed guide lines from unknown sample to both axes
fig.add_shape(
type="line",
x0=unknown_concentration,
y0=0,
x1=unknown_concentration,
y1=unknown_absorbance,
line={"color": RED, "width": 1.5, "dash": "dash"},
)
fig.add_shape(
type="line",
x0=0,
y0=unknown_absorbance,
x1=unknown_concentration,
y1=unknown_absorbance,
line={"color": RED, "width": 1.5, "dash": "dash"},
)
# Regression equation and R² annotation — placed in lower-right area clear of legend
fig.add_annotation(
x=0.97,
y=0.06,
xref="paper",
yref="paper",
text=f"<b>y = {slope:.4f}x + {intercept:.4f}</b><br>R² = {r_squared:.5f}",
showarrow=False,
font={"size": 16, "color": INK, "family": "Arial, sans-serif"},
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderwidth=1,
borderpad=10,
align="right",
xanchor="right",
yanchor="bottom",
)
# Layout
fig.update_layout(
autosize=False,
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
title={
"text": title,
"font": {"size": title_fontsize, "color": INK, "family": "Arial, sans-serif"},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Concentration (mg/L)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [-0.5, 15.5],
"showgrid": False,
"zeroline": False,
"linecolor": INK_SOFT,
"linewidth": 1,
"ticks": "outside",
"tickcolor": INK_SOFT,
},
yaxis={
"title": {"text": "Absorbance", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"range": [-0.05, 0.75],
"gridcolor": GRID,
"gridwidth": 1,
"zeroline": False,
"linecolor": INK_SOFT,
"linewidth": 1,
"ticks": "outside",
"tickcolor": INK_SOFT,
},
legend={
"font": {"size": 10, "color": INK_SOFT},
"x": 0.02,
"y": 0.98,
"xanchor": "left",
"yanchor": "top",
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
margin={"l": 80, "r": 40, "t": 80, "b": 60},
)
# Save — landscape 3200×1800 (width=800, height=450, scale=4)
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Beer-Lambert Calibration Curve on anyplot.ai.