G = GM / r² Calculator

Calculate gravitational values with flexible variable solving. Export results, review examples, and understand each step clearly for dependable problem solving.

Calculator Form

Plotly Graph

This graph shows how g changes with radius using the latest working values.

Example Data Table

Case G M r Calculated g
Earth surface 6.67430e-11 5.972e24 6.371e6 9.82 m/s²
Moon surface 6.67430e-11 7.342e22 1.7374e6 1.62 m/s²
Mars surface 6.67430e-11 6.4171e23 3.3895e6 3.73 m/s²

Formula Used

The main formula is:

g = GM / r²

Where g is gravitational field strength, G is the gravitational constant, M is the mass creating the field, and r is the distance from the mass center.

Rearranged forms:

  • G = gr² / M
  • M = gr² / G
  • r = √(GM / g)

How to Use This Calculator

  1. Select which variable you want to solve.
  2. Enter the known values in the other fields.
  3. Use scientific notation when needed.
  4. Press the calculate button.
  5. Read the result above the form.
  6. Use CSV or PDF export if needed.
  7. Review the graph to see how radius affects g.

About This Calculator

This calculator helps users evaluate the relationship between gravitational field strength, mass, distance, and the universal gravitational constant. It supports direct solving for any one unknown variable. That makes it useful for practice, homework checking, quick engineering estimates, and general science learning.

The interface keeps the layout simple while still offering strong functionality. Users can enter values in standard or scientific notation, calculate instantly, inspect a graph, and save a short working history in the same session. The export options make it easier to document results for reports or assignments.

Although your request places this tool in Chemistry, the equation itself comes from gravitation and classical physics. Still, it can support chemistry-adjacent learning in physical science courses where unit analysis, notation, and scientific constants are important. The graph section adds a practical visual view of the inverse-square relationship.

The example table provides familiar planetary references, helping users compare outputs with known values. This builds confidence and gives a starting point for further testing. The FAQ section below answers common questions in plain language, without hidden panels, so readers can scan the page easily.

Frequently Asked Questions

1. What does g represent in this calculator?

g represents gravitational field strength or gravitational acceleration at a chosen distance from the mass center. It is commonly expressed in meters per second squared.

2. Can I solve for radius with this tool?

Yes. Choose r in the solve field, then enter g, G, and M. The calculator will apply the square root form of the equation automatically.

3. Can I use scientific notation?

Yes. Values like 6.67430e-11 or 5.972e24 are accepted. This is useful because gravitational constants and planetary masses are very large or very small.

4. Why does g decrease when r increases?

Because the equation uses an inverse-square relationship. When distance doubles, gravitational field strength becomes one quarter of its previous value.

5. What units should I use?

Use g in m/s², G in N·m²/kg², M in kilograms, and r in meters. Consistent units help produce correct results.

6. Why does the calculator show an input error?

The message appears when required fields are empty, nonnumeric, zero where not allowed, or negative when the chosen variable needs positive values.

7. What does the graph display?

The graph plots radius on the horizontal axis and gravitational field strength on the vertical axis using the latest valid constants and mass values.

8. Is the saved history permanent?

No. The history is stored in the current session only. It helps with short-term review and can be exported to CSV or PDF.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.