Atom Calculator

Calculate the number of protons, neutrons, electrons, mass number, atomic number, and charge of any atom or ion. Select an element or enter known values to find the missing atomic properties.

Selecting an element auto-fills the atomic number. You can also enter values manually.
Number of protons in the nucleus (defines the element)
Total number of protons + neutrons in the nucleus
Neutral particles in the nucleus (N = A - Z)
Negative particles orbiting the nucleus
Net charge = Protons - Electrons (0 for neutral atoms, positive for cations, negative for anions)

Calculated Results

Element
--
Atomic Number (Z)
--
protons
Mass Number (A)
--
nucleons
Protons
--
p+
Neutrons
--
n0
Electrons
--
e-
Charge
--
Ion Type
--
Electron Config
--
shell configuration

What Is an Atom?

An atom is the fundamental building block of all matter in the universe. Everything you see around you, from the air you breathe to the device you are reading this on, is composed of atoms. The word "atom" comes from the ancient Greek word atomos, meaning "uncuttable" or "indivisible." The Greek philosopher Democritus first proposed around 400 BCE that matter could be divided into smaller and smaller pieces until one reached the smallest possible unit, which he called an atom. While we now know that atoms themselves are composed of even smaller subatomic particles, the atom remains the smallest unit of an element that retains the chemical properties of that element.

An atom consists of a dense central region called the nucleus and a surrounding cloud of electrons. The nucleus contains two types of particles: protons, which carry a positive electrical charge, and neutrons, which carry no charge at all. Electrons, which are negatively charged, orbit the nucleus at various energy levels or "shells." The nucleus is incredibly small compared to the overall size of the atom. If an atom were the size of a football stadium, the nucleus would be about the size of a marble at the center, yet it contains more than 99.9% of the atom's total mass.

The number of protons in the nucleus determines which element the atom belongs to. For instance, every atom with 1 proton is hydrogen, every atom with 6 protons is carbon, and every atom with 79 protons is gold. This number is called the atomic number and is denoted by the letter Z. The total number of protons and neutrons together gives the mass number, denoted by A. In a neutral atom, the number of electrons equals the number of protons, resulting in no net electrical charge. When an atom gains or loses electrons, it becomes an ion with a net charge.

n = 3 (M shell) n = 2 (L shell) n = 1 (K shell) p+ p+ p+ p+ n n n n Proton (p+) Neutron (n) Electron (e-) Shell

Simplified diagram of an atom with 4 protons, 4 neutrons, and 6 electrons (showing animated orbital paths)

Subatomic Particles: The Building Blocks of Atoms

Every atom is made up of three fundamental subatomic particles: protons, neutrons, and electrons. Each of these particles has distinct properties that determine the identity, mass, and behavior of the atom. Understanding these particles is essential for studying chemistry, physics, and virtually every branch of science.

Protons

Protons are positively charged particles found inside the nucleus of every atom. Each proton carries a charge of +1 elementary charge (approximately +1.602 x 10-19 coulombs). The mass of a proton is approximately 1.007 atomic mass units (amu), or about 1.673 x 10-27 kilograms. The number of protons in an atom's nucleus is called the atomic number (Z), and it uniquely identifies the element. For example, hydrogen always has 1 proton, helium always has 2 protons, and uranium always has 92 protons. If you change the number of protons, you change the element entirely. This is why protons are considered the defining characteristic of an element.

Protons are themselves composite particles, made up of even smaller entities called quarks. Specifically, each proton consists of two "up" quarks and one "down" quark, held together by the strong nuclear force mediated by particles called gluons. Protons are remarkably stable; a free proton has never been observed to decay, and the proton's half-life is estimated to be greater than 1034 years, far exceeding the current age of the universe.

Neutrons

Neutrons are electrically neutral particles, meaning they carry no charge. They reside in the nucleus alongside protons. The mass of a neutron is approximately 1.009 amu, slightly heavier than a proton. Neutrons serve a critical role in atomic stability: they help to offset the electromagnetic repulsion between the positively charged protons in the nucleus. Without neutrons, the positively charged protons would repel each other and the nucleus would fly apart. The strong nuclear force, which is the strongest of the four fundamental forces, binds neutrons and protons together in the nucleus.

Like protons, neutrons are composed of quarks, specifically one "up" quark and two "down" quarks. Unlike protons, free neutrons are unstable and undergo beta decay with a half-life of about 10.2 minutes, converting into a proton, an electron, and an antineutrino. However, when bound inside a nucleus, neutrons can be stable for the lifetime of the atom.

Electrons

Electrons are negatively charged particles that orbit the nucleus in regions called electron shells or energy levels. Each electron carries a charge of -1 elementary charge (approximately -1.602 x 10-19 coulombs). The mass of an electron is approximately 1/1836 amu, or about 9.109 x 10-31 kilograms, making it nearly 2000 times lighter than a proton or neutron. Due to their tiny mass, electrons contribute very little to the overall mass of an atom but play a crucial role in chemical bonding, electrical conductivity, and nearly all chemical reactions.

Electrons do not orbit the nucleus in neat circular paths like planets around the sun. Instead, they exist in orbitals, which are probability regions where the electron is most likely to be found. These orbitals have different shapes (s, p, d, f) and energy levels. The arrangement of electrons in these orbitals is called the electron configuration, and it determines how an atom interacts with other atoms to form chemical bonds.

Particle Symbol Charge Mass (amu) Location
Proton p+ +1 ~1.007 Nucleus
Neutron n0 0 ~1.009 Nucleus
Electron e- -1 ~0.00055 Electron shells

Atomic Number: The Identity of an Element

The atomic number, denoted by the letter Z, is the number of protons found in the nucleus of an atom. It is the single most important property of an element because it defines which element the atom is. No two different elements have the same atomic number. The periodic table of elements is organized in order of increasing atomic number, from hydrogen (Z = 1) to oganesson (Z = 118).

The atomic number determines the element's position on the periodic table and, consequently, its chemical properties. Elements in the same column (group) of the periodic table have similar chemical behaviors because they have the same number of valence (outermost) electrons. For example, all alkali metals (lithium, sodium, potassium, etc.) have one valence electron, which is why they are all highly reactive and form +1 ions readily.

Atomic Number (Z) = Number of Protons Z = Number of Electrons (for neutral atoms only)

In a neutral atom, the number of electrons equals the number of protons, so the atomic number also tells you how many electrons the atom has. However, if the atom is an ion (has gained or lost electrons), the number of electrons will differ from the atomic number. Despite this, the atomic number and the identity of the element remain unchanged because the number of protons has not changed.

Mass Number: Counting Nucleons

The mass number, denoted by A, is the total count of protons and neutrons (collectively called nucleons) in an atom's nucleus. It is always a whole number and provides a close approximation of the atom's actual mass in atomic mass units. The mass number is calculated using the formula:

Mass Number (A) = Protons (Z) + Neutrons (N) A = Z + N N = A - Z

It is important to distinguish the mass number from the atomic mass (also called atomic weight). The mass number is always an integer because it is simply a count of particles. The atomic mass, on the other hand, is a weighted average of the masses of all naturally occurring isotopes of an element and is typically a decimal number. For example, carbon has a mass number of 12 (for its most common isotope, Carbon-12), but its atomic mass listed on the periodic table is approximately 12.011 amu because it accounts for the small natural abundance of Carbon-13 and Carbon-14 isotopes.

Example: Oxygen-16

Oxygen has an atomic number of 8 (Z = 8), meaning it has 8 protons. The most common isotope of oxygen has a mass number of 16 (A = 16). Therefore:

Neutrons = A - Z = 16 - 8 = 8 neutrons

A neutral oxygen atom also has 8 electrons, and its charge is 0.

Isotopes: Same Element, Different Mass

Isotopes are atoms of the same element (same number of protons) that have different numbers of neutrons, and therefore different mass numbers. All isotopes of a given element behave almost identically in chemical reactions because chemical behavior is determined primarily by the number and arrangement of electrons, which in turn is determined by the number of protons. However, isotopes can differ significantly in their nuclear stability.

Some isotopes are stable, meaning their nuclei do not change over time. Others are radioactive (also called radioisotopes), meaning their nuclei are unstable and will eventually decay by emitting radiation. The rate of this decay is characterized by the isotope's half-life, which is the time it takes for half of a given sample of the isotope to decay.

Notable Isotope Examples

Isotope Protons (Z) Neutrons (N) Mass Number (A) Stable? Notes
Carbon-12 6 6 12 Yes Most common carbon isotope (98.9%)
Carbon-13 6 7 13 Yes Used in NMR spectroscopy (1.1%)
Carbon-14 6 8 14 No Radioactive; used in carbon dating (half-life ~5730 years)
Hydrogen-1 1 0 1 Yes Most common hydrogen isotope (protium)
Hydrogen-2 1 1 2 Yes Deuterium; used in heavy water
Hydrogen-3 1 2 3 No Tritium; radioactive (half-life ~12.3 years)
Uranium-235 92 143 235 No Fissile material used in nuclear reactors and weapons
Uranium-238 92 146 238 No Most common uranium isotope (99.3%)

Ions: Charged Atoms

An ion is an atom or molecule that has gained or lost one or more electrons, giving it a net electrical charge. Because the number of protons remains unchanged, the identity of the element does not change when it becomes an ion. Only the number of electrons changes.

Cations (Positive Ions)

When an atom loses one or more electrons, it has more protons than electrons, resulting in a net positive charge. Such ions are called cations. Metals commonly form cations because they have relatively low ionization energies and tend to lose their valence electrons easily. For example:

Anions (Negative Ions)

When an atom gains one or more electrons, it has more electrons than protons, resulting in a net negative charge. Such ions are called anions. Nonmetals commonly form anions because they have high electron affinities and tend to gain electrons to complete their outer electron shell. For example:

Charge (Q) = Number of Protons - Number of Electrons Q = Z - e If Q > 0 → Cation (positive ion, lost electrons) If Q < 0 → Anion (negative ion, gained electrons) If Q = 0 → Neutral atom

How to Calculate Atomic Properties: Step-by-Step Guide

Calculating the atomic properties of an atom or ion is straightforward once you understand the relationships between protons, neutrons, electrons, atomic number, mass number, and charge. Below is a step-by-step guide with examples to help you master these calculations.

Step 1: Identify What You Know

Start by identifying which values you have been given. You typically need at least two of the following to calculate the rest: atomic number (Z), mass number (A), number of neutrons (N), number of electrons (e), or charge (Q).

Step 2: Use the Key Relationships

The four key formulas you need:

  1. Atomic Number (Z) = Number of Protons - These are always the same thing.
  2. Mass Number (A) = Z + N - Total nucleons equals protons plus neutrons.
  3. Neutrons (N) = A - Z - Rearranged from the formula above.
  4. Charge (Q) = Z - e - Net charge equals protons minus electrons.

For a neutral atom: Q = 0, so e = Z (electrons equal protons).

Step 3: Calculate the Missing Values

Use the known values and the formulas above to find whatever is unknown. Let us work through several examples to demonstrate.

Example 1: Neutral Sodium Atom

Given: Sodium (Na), Atomic Number Z = 11, Mass Number A = 23

Find: Protons, Neutrons, Electrons, Charge

  • Protons = Z = 11
  • Neutrons = A - Z = 23 - 11 = 12
  • Since it is neutral, Electrons = Protons = 11
  • Charge = Z - e = 11 - 11 = 0

Example 2: Chloride Ion (Cl-)

Given: Chlorine, Z = 17, A = 35, Charge = -1

Find: Protons, Neutrons, Electrons

  • Protons = Z = 17
  • Neutrons = A - Z = 35 - 17 = 18
  • Charge = Z - e, so -1 = 17 - e, therefore e = 18

Example 3: Finding Mass Number from Neutrons

Given: An atom has 26 protons and 30 neutrons

Find: Element, Mass Number, Electrons (neutral), Charge

  • Z = 26, so the element is Iron (Fe)
  • A = Z + N = 26 + 30 = 56
  • If neutral: Electrons = Protons = 26
  • Charge = 26 - 26 = 0

Electronic Configuration Basics

The electron configuration of an atom describes how its electrons are distributed among the various atomic orbitals. Understanding electron configuration is essential for predicting an element's chemical behavior, bonding properties, and position in the periodic table.

Electrons fill orbitals according to three fundamental rules:

  1. Aufbau Principle: Electrons fill the lowest energy orbitals first before moving to higher energy levels. The general filling order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, and so on.
  2. Pauli Exclusion Principle: Each orbital can hold a maximum of 2 electrons, and they must have opposite spins (one spin-up and one spin-down).
  3. Hund's Rule: When filling orbitals of equal energy (degenerate orbitals), electrons occupy them singly first with parallel spins before pairing up.

Each electron shell (principal energy level) can hold a maximum number of electrons given by the formula 2n2, where n is the shell number:

Shell n Max Electrons (2n2) Subshells
K 1 2 1s
L 2 8 2s, 2p
M 3 18 3s, 3p, 3d
N 4 32 4s, 4p, 4d, 4f

Example: Electron Configuration of Oxygen (Z = 8)

Oxygen has 8 electrons. They fill as follows:

1s2 2s2 2p4

This means 2 electrons in the 1s orbital, 2 in the 2s orbital, and 4 in the 2p orbitals. The shorthand shell notation is [2, 6], meaning 2 electrons in the first shell and 6 in the second.

Electron configuration is directly related to an element's position on the periodic table. Elements in the same group have similar valence electron configurations, which explains their similar chemical properties. For example, all noble gases have completely filled outer shells, making them extremely stable and unreactive.

Frequently Asked Questions

What is the difference between atomic number and mass number? +

The atomic number (Z) is the number of protons in an atom's nucleus and defines which element the atom is. The mass number (A) is the total number of protons plus neutrons in the nucleus. Two atoms of the same element always have the same atomic number but can have different mass numbers if they have different numbers of neutrons (making them isotopes).

How do I find the number of neutrons in an atom? +

Subtract the atomic number from the mass number: Neutrons = Mass Number (A) - Atomic Number (Z). For example, for Carbon-14: Neutrons = 14 - 6 = 8 neutrons.

What makes an atom become an ion? +

An atom becomes an ion when it gains or loses electrons. If it loses electrons, it becomes a positively charged ion called a cation. If it gains electrons, it becomes a negatively charged ion called an anion. The number of protons does not change, so the element remains the same.

Can the number of protons in an atom change? +

Under normal chemical conditions, no. The number of protons defines the element and only changes during nuclear reactions such as radioactive decay, nuclear fission, or nuclear fusion. For instance, during beta decay, a neutron converts to a proton (or vice versa), changing the element. Alchemists historically tried to change lead (82 protons) into gold (79 protons), but this requires nuclear transmutation, not chemical reactions.

Why do some atoms have more neutrons than protons? +

As the atomic number increases, more neutrons are needed to stabilize the nucleus against the growing electromagnetic repulsion between protons. For light elements (like carbon and oxygen), the number of neutrons roughly equals the number of protons. For heavier elements (like lead or uranium), there are significantly more neutrons than protons. This is because the strong nuclear force that holds the nucleus together has a short range, so additional neutrons are needed to provide extra binding without adding more repulsive positive charge.

What is an isotope? +

An isotope is a variant of an element that has the same number of protons but a different number of neutrons. Isotopes of the same element have identical chemical properties but different masses. Some isotopes are stable, while others are radioactive. For example, Carbon-12 (6 protons, 6 neutrons) and Carbon-14 (6 protons, 8 neutrons) are both isotopes of carbon, but Carbon-14 is radioactive and is used in radiocarbon dating.

How does the calculator determine the electron configuration? +

The calculator uses the Aufbau principle to fill electron orbitals in order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. It distributes the total number of electrons across these subshells, respecting the maximum occupancy of each (s = 2, p = 6, d = 10, f = 14). The result is a standard electron configuration string like "1s2 2s2 2p6 3s2 3p6" for argon (18 electrons).

What is the difference between atomic mass and mass number? +

The mass number is always a whole number representing the total count of protons and neutrons in a specific isotope. The atomic mass (or atomic weight) is a weighted average of the masses of all naturally occurring isotopes of an element, and it is almost always a decimal number. For instance, chlorine's mass number is either 35 or 37 (for its two stable isotopes), but its atomic mass on the periodic table is about 35.45 amu because Cl-35 is about three times more abundant than Cl-37.

Can an atom have zero neutrons? +

Yes. The most common isotope of hydrogen, called protium (Hydrogen-1), has 1 proton and 0 neutrons. It is the only stable atom that has no neutrons in its nucleus. All other elements require at least one neutron to maintain nuclear stability.