Force of Gravity Between Two Objects Calculator

Enter two masses and exact separation distance. Get force, field strength, and instant unit conversions. Explore gravity calculations with examples, exports, and physics notes.

Calculator

Formula Used

F = G × m₁ × m₂ ÷ r²

F is the gravitational force in newtons. G is the gravitational constant. m₁ and m₂ are masses in kilograms. r is the center distance in meters.

a₁ = F ÷ m₁ and a₂ = F ÷ m₂

These values show the acceleration caused by the same attractive force.

U = -G × m₁ × m₂ ÷ r

U is gravitational potential energy. The negative sign shows an attractive bound interaction.

How to Use This Calculator

  1. Enter a name for each object if needed.
  2. Enter the mass of both objects.
  3. Select the correct mass unit for each object.
  4. Enter the center to center distance.
  5. Select the distance unit.
  6. Keep the default gravitational constant for standard work.
  7. Choose the output precision.
  8. Press the calculate button.
  9. Use CSV or PDF export to save the result.

Example Data Table

Example Mass 1 Mass 2 Distance Force
Earth and Moon 5.9722E+24 kg 7.3420E+22 kg 3.8440E+8 m 1.9806E+20 N
Earth and Sun 5.9722E+24 kg 1.9885E+30 kg 1.4960E+11 m 3.5417E+22 N
Two 70 kg people 70 kg 70 kg 1 m 3.2704E-7 N
Two 1000 kg cars 1000 kg 1000 kg 5 m 2.6697E-6 N

Gravity And Two Object Attraction

Gravity is the mutual pull between masses. Every object with mass attracts every other object. The pull is tiny for daily objects. It becomes large for planets, moons, stars, and heavy machines. Newton's law gives a useful estimate. It treats each object as a point mass. It also works for round bodies when distance is measured between centers.

Why Distance Matters

Distance has a squared effect. Doubling the center distance makes the force four times smaller. Tripling it makes the force nine times smaller. This is the inverse square rule. It explains why nearby masses can matter more than distant ones. The calculator converts each distance unit to meters before applying the formula. This keeps the physics consistent.

Advanced Inputs And Outputs

This tool accepts common mass units. You can enter kilograms, grams, pounds, slugs, or astronomical masses. It also accepts many distance units. You may use meters, feet, miles, kilometers, or astronomical units. A custom gravitational constant is included for advanced checks. Most users should keep the official standard value. The result appears in newtons. Extra lines show acceleration on each object and gravitational potential energy.

Practical Uses

Students can test homework examples. Teachers can prepare quick demonstrations. Engineers can compare small attraction forces between large components. Astronomy learners can compare Earth, Moon, and Sun scale forces. The calculation is ideal for center to center separation. For wide or irregular objects, treat the result as an approximation. More detailed models may require integration or simulation.

Reading The Result

The force is attractive. Both objects feel the same force magnitude. Their accelerations are different when their masses differ. The lighter object accelerates more. The heavier object accelerates less. This does not break Newton's third law. It simply follows acceleration equals force divided by mass. Very small answers often use scientific notation. That format is normal for gravity problems.

Good Measurement Practice

Use realistic units and clear center distances. Avoid zero or negative values. Check whether the given distance is surface gap or center distance. Add radii when the problem gives a gap between surfaces. Record the chosen units with the answer. This makes the result easier to verify.

Store exported files with notes for review.

FAQs

What does this calculator find?

It finds the attractive gravitational force between two masses. The answer is shown in newtons. It also shows related acceleration and potential energy values.

Which distance should I enter?

Use the center to center distance between the two objects. For spheres, measure from one center to the other center.

Can I use pounds for mass?

Yes. Select pounds from the mass unit menu. The calculator converts pounds to kilograms before using Newton's formula.

Why is my answer very small?

Gravity is weak between everyday objects. Small masses and large distances often produce tiny forces. Scientific notation helps display those values clearly.

Should I change the gravitational constant?

Most users should keep the default value. Change it only for special models, classroom tests, or controlled comparison problems.

Do both objects feel the same force?

Yes. Both objects feel the same force magnitude. Their accelerations differ because acceleration depends on each object's mass.

Can this be used for planets?

Yes. It works well for planets, moons, and stars when you use center distances and correct masses.

Is this exact for irregular objects?

It is an approximation for irregular shapes. Complex objects may need a more detailed mass distribution model.

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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.