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How to Treat Physical Constants in Different Sig Fig Conventions (AP, IB, ASTM, GUM)

Physical constants are not all exact: AP and IB treat exam-sheet constants as sufficiently precise, ASTM E29 governs conformance rounding, and the GUM governs uncertainty reporting. Learn the rules, citations, and pitfalls.

Written by Tommy C. MoranPublished November 10, 2026

Short Answer

Quick Facts

Exact constants	c, h, e, k, and N_A are exact under the SI and have infinite significant figures.
AP convention	Use constants from the equation sheet; final sig figs are limited by measured data, not the constant.
IB convention	Data Booklet constants are given to 3+ sig figs and are not usually the limiting factor.
ASTM E29	Applies to conformance rounding, not physical constants; ties round to even (Clause 6).
GUM	Report uncertainty to 1-2 significant figures (JCGM 100:2008, 7.2.6).
ISO 80000-1	General rounding ties go to the nearest even digit (Clause 5.4.3).
Measured constants	G and m_e have CODATA uncertainties; propagate them when they limit the result.
Common error	Rounding constants before intermediate steps causes double-rounding error.

Physical constants are the fixed anchors of quantitative science, but they are not all treated the same way in significant-figure conventions. Some are exact by definition in the International System of Units (SI); others are measured values with uncertainties published by CODATA. Exam boards such as AP and IB, standards bodies such as ASTM and ISO, and metrology guides such as the GUM each handle constants differently. This article is part of our precision-and-rounding reference, not just a calculator page: it explains the rules, cites the standards, and shows how to avoid common errors.

Rule Statement: Constants Are Not All Equal

The first rule is to classify the constant. A defined constant has an exact value under the SI, such as the speed of light in vacuum c = 299 792 458 m/s, Planck constant h = 6.626 070 15 × 10^-34 J s, elementary charge e = 1.602 176 634 × 10^-19 C, Boltzmann constant k = 1.380 649 × 10^-23 J/K, and Avogadro constant N_A = 6.022 140 76 × 10²³ mol^-1. These have infinite significant figures and should not limit a calculation. A measured constant, such as the gravitational constant G = 6.674 30(15) × 10^-11 m³ kg^-1 s^-2, has a finite uncertainty. Its precision matters when it is the limiting factor.

Second, follow the convention in use. AP and IB are educational exam conventions. ASTM E29 and ISO 80000-1 are documentary standards for rounding and significant digits. The GUM is a metrological guide for expressing uncertainty. They answer different questions.

AP convention

In AP Physics and AP Chemistry, constants on the official equation and constants sheets are provided so students do not memorize them. They are treated as sufficiently precise for the problem. The final answer is normally limited by the least number of significant figures in the measured data, not by the constant. For example, if a time is 2.5 s (two significant figures) and c is 3.00 × 10⁸ m/s (three significant figures), the result should have two significant figures.

IB convention

IB Data Booklets give constants to three or more significant figures. IB assessments expect final answers to be consistent with the precision of the data. Constants from the booklet are not usually the limiting factor. Carry the full booklet value through intermediate steps and round only at the end. Avoid replacing N_A = 6.02 × 10²³ mol^-1 with 6.0 × 10²³ unless the problem explicitly requires it.

ASTM E29

ASTM E29-13, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, does not establish a convention for physical constants. It tells you how to round observed or calculated test values before comparing them with a specification limit. Clause 6 specifies round-to-nearest, with ties resolved to the nearest even digit. This is the same tie rule found in ISO 80000-1:2009, Clause 5.4.3.

GUM

The GUM, JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement, treats constants as inputs to a measurement model. If a constant is exact, its uncertainty is zero. If it is measured, its uncertainty must be propagated. Clause 7.2.6 recommends reporting the uncertainty to one or two significant figures and rounding the measured value to the same decimal place.

Worked Examples

Example 1: AP Physics — speed of light

Problem: A pulse travels for 2.5 s at c = 3.00 × 10⁸ m/s. Find the distance.

Step 1: Multiply: 3.00 × 10⁸ m/s × 2.5 s = 7.50 × 10⁸ m. Step 2: Identify significant figures. The time 2.5 s has two significant figures. The constant has three. Step 3: Round to the least precise measurement: 7.5 × 10⁸ m. The constant did not limit the answer.

Example 2: IB Chemistry — Avogadro constant

Problem: Calculate the number of particles in 0.0500 mol using N_A = 6.02 × 10²³ mol^-1.

Step 1: Multiply: 0.0500 mol × 6.02 × 10²³ mol^-1 = 3.010 × 10²². Step 2: The amount 0.0500 mol has three significant figures; the booklet constant has three. Step 3: Report 3.01 × 10²² particles. If the booklet gives 6.022 × 10²³, still report three significant figures because the measured amount limits the result.

Example 3: GUM — measured constant with uncertainty

Problem: A measured value of a local gravitational acceleration is 9.812 m/s² with standard uncertainty 0.023 m/s². Report according to GUM Clause 7.2.6.

Step 1: Round the uncertainty to two significant figures: 0.023. Step 2: Round the value to the same decimal place: 9.812. Step 3: Report 9.812 ± 0.023 m/s². If the uncertainty were 0.123, it would become 0.12, and the value would be 9.81.

Example 4: ASTM E29 — conformance rounding

Problem: A specification limit is 10.00. A test result is 10.005. Does it conform?

Step 1: ASTM E29 Clause 6 uses round half to even. The digit before the 5 is 0, which is even, so 10.005 rounds to 10.00. Step 2: Compare with the limit. The rounded value equals 10.00 and conforms. If the test result were 10.015, it would round to 10.02 and fail the upper limit.

Counter-Examples

Letting an exact constant set the precision. Using c = 299 792 458 m/s as an excuse to report ten significant figures when the time is 2.5 s is wrong. The measurement limits the result.
Using a remembered constant instead of the provided one. Replacing the IB Data Booklet value N_A = 6.02 × 10²³ with 6.0 × 10²³ adds artificial uncertainty and can change the final significant figures.
Premature rounding. Rounding π to 3.14 before a multi-step calculation, or rounding h before a final division, creates double-rounding error. Keep guard digits.
Mixing tie rules. ASTM E29 and ISO 80000-1 use round half to even. Many AP and IB classroom rules use round half up. Do not apply ASTM E29 tie-breaking to an AP exam unless instructed.
Over-reporting GUM uncertainty. Writing 9.812 ± 0.02345 m/s² ignores the GUM recommendation to use one or two significant figures for the uncertainty.

Convention Comparison Table

Convention	Treatment of constants	Rounding tie rule	Final significant figures	Key citation
AP	Constants on equation sheet are given values; use as needed	Usually round half up; no formal tie rule	Least significant figures in measured data	AP Physics 1 and AP Chemistry Equations and Constants sheets
IB	Data Booklet constants to 3+ significant figures; not limiting unless stated	Standard rounding; avoid premature rounding	Consistent with data; often 3 significant figures	IB Physics and Chemistry Data Booklets
ASTM E29	Not a constant convention; applies to test data conformance	Round half to even	To specified limit	ASTM E29-13, Clause 6
GUM	Exact constants have zero uncertainty; measured constants use CODATA	Uncertainty to 1-2 significant figures	Value to same decimal as uncertainty	JCGM 100:2008, Clause 7.2.6
ISO 80000-1	General quantity and unit rules; exact constants infinite	Round half to even	Based on uncertainty	ISO 80000-1:2009, Clause 5.4.3

Standards Citation

Use these primary sources when precision matters. ASTM E29-13, Clause 6, specifies rounding for conformance with specifications. JCGM 100:2008 (GUM), Clause 7.2.6, gives the one-or-two-significant-figure recommendation for uncertainty. ISO 80000-1:2009, Clause 5.4.3, provides general rounding rules, including ties to even. NIST SP 811, Clause 7.9, is the U.S. guide for SI usage and rounding. NIST CODATA 2018 is the authoritative source for measured fundamental constants and their uncertainties. AP and IB are not standards bodies, but their equation sheets and data booklets define the exam expectations.

Common Mistakes

Assuming every constant is exact. Only defined constants are exact. Measured constants like G carry uncertainty.
Letting a high-precision constant dictate the answer. The least precise measurement normally controls the final significant figures.
Rounding constants before the final step. Carry full precision through intermediate calculations to avoid double-rounding error.
Applying ASTM E29 to exam sig figs. ASTM E29 is for conformance testing, not AP or IB answer formatting.
Ignoring CODATA uncertainty. When a measured constant limits the result, include its uncertainty in the propagation.
Reporting too many digits in GUM uncertainty. Two significant figures for uncertainty is usually the maximum; one is often sufficient.

Quick Reference Table

Constant	Status	Typical value	Significant-figures guidance
Speed of light c	Exact (SI)	299 792 458 m/s	Infinite significant figures; use as exact
Planck constant h	Exact (SI)	6.626 070 15 × 10^-34 J s	Exact; use full value
Avogadro constant N_A	Exact (SI)	6.022 140 76 × 10²³ mol^-1	Exact; use full value
Gravitational constant G	Measured	6.674 30(15) × 10^-11 m³ kg^-1 s^-2	Use CODATA uncertainty; often 3-4 significant figures
Electron mass m_e	Measured	9.109 383 7015(28) × 10^-31 kg	Use CODATA; uncertainty in parentheses

Exact Numbers — defined constants have infinite significant figures.
Significant Figures — core counting and rounding rules.
GUM Guide — uncertainty reporting and propagation.
ASTM E29 — conformance rounding and tie-breaking.
ISO 80000 — quantity, unit, and rounding standards.
Why Sig Figs Are an Approximation — limits of significant-figure rules.

Sources & Further Reading

JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), Clause 7.2.6.
ASTM E29-13, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications, Clause 6.
ISO 80000-1:2009, Quantities and units — Part 1: General, Clause 5.4.3.
NIST SP 811, Guide for the Use of the International System of Units (SI), Clause 7.9.
NIST CODATA 2018, Fundamental Physical Constants.
College Board AP Physics 1 and AP Chemistry Equations and Constants sheets.
IB Physics and Chemistry Data Booklets.

FAQ

Are physical constants exact?

Some are exact by SI definition, including c, h, e, k, and N_A. Others, such as G, are measured and have uncertainty. NIST CODATA publishes the recommended values.

How many significant figures should I use for a constant in AP or IB?

Use the value provided on the equation sheet or data booklet. Do not let it limit the final answer unless the problem states otherwise. The least precise measured data determines the final significant figures.

Does GUM require rounding constants?

GUM focuses on uncertainty. Report uncertainty to one or two significant figures (JCGM 100:2008, Clause 7.2.6). Use constants with sufficient precision, often from CODATA, and propagate their uncertainty if they are measured.

Should I round constants before calculating?

No. Carry full precision through intermediate steps and round only the final result. Premature rounding causes double-rounding error and can shift the last digit.