Calculate Average Force
Use a signed free energy change and a positive displacement magnitude. The direction selector gives the displacement its coordinate sign.
Example Data Table
| Free energy input | Displacement and direction | Calculated force |
|---|---|---|
| −30 kJ/mol | 1 nm, increasing coordinate | +49.82 pN |
| 60 eV per system | 2 nm, increasing coordinate | −4.81 nN |
| 0.012 J per system | 0.30 m, increasing coordinate | −0.040 N |
Formula Used
F = −ΔG / Δx
- F is the average force along the selected coordinate.
- ΔG is the change in free energy for the chosen path segment.
- Δx is the signed displacement along that coordinate.
- The negative sign shows that force points toward lower free energy.
- For a continuously changing profile, the local form is F = −dG/dx.
- Molar energy is divided by Avogadro’s constant before force is calculated.
How to Use This Calculator
- Enter the free energy change. Keep its physical sign.
- Select the energy unit and choose whether the value is per system or per mole.
- Enter the nonzero displacement magnitude across the same path segment.
- Select the displacement unit and the coordinate direction.
- Choose an output force unit and a display precision.
- Press Calculate Force. Read the sign as a direction relative to your selected coordinate.
- Use CSV or PDF after calculating to save the result.
Force from Free Energy Explained
Free energy describes energy that can perform useful work at constant temperature and pressure. A difference in free energy along a path can create an average driving force. This calculator converts that energy difference and path length into force. It suits molecular motion, chemical reactions, and biological motors. The result is average. It does not automatically describe every changing force along a curved or irregular path.
The relationship is F equals negative delta G divided by delta x. Delta G is the energy change. Delta x is the signed displacement along the selected coordinate. The sign matters. Systems naturally move toward lower free energy. When the coordinate increases and free energy decreases, the calculated force is positive. It points forward. A positive free energy increase gives a negative force here.
This calculation works best when free energy changes nearly linearly over the distance. For a changing energy landscape, use a short interval. This improves local force estimates. In calculus form, force is negative dG divided by dx. The derivative measures the local free energy slope. The calculator uses the finite difference form because many practical datasets contain measured changes between two positions.
Choose the energy basis carefully. A single input uses energy for one system. A molar input first converts energy per mole into energy per particle. The conversion divides by Avogadro's constant. This is essential. A value written in kilojoules per mole cannot be divided by nanometers directly without changing the basis. The calculator handles this conversion before force.
Units keep the answer easy to interpret. One newton equals one joule per meter. Small systems often produce pico or nano newton forces. Large systems may use newtons or milli newtons. Select an output unit that keeps the displayed number readable. The signed value retains its meaning. A plus sign follows positive coordinate. A minus sign means the force points opposite to it.
The path direction setting creates a signed displacement. Select increasing coordinate for forward motion. Select decreasing coordinate when it moves backward. This choice changes the sign of delta x. It therefore changes the sign of the reported force. It does not change the physical energy difference. State the coordinate convention when sharing results or comparing data.
Check the assumptions before using the number in a design decision. Temperature and pressure remain implicit in the free energy value. Friction, viscosity, random thermal motion, and mechanical constraints may affect measured motion. The calculated force represents an energy gradient. It is not always the same as a direct load cell reading. Use it with experimental context and an appropriate physical model in practice.
For reliable results, enter a nonzero displacement and a consistent energy basis. Use more decimal places for very small lengths. Compare several short path segments when the energy profile bends sharply. Record the selected units with every result. Accurate inputs create forces you can interpret confidently today.
Frequently Asked Questions
1. What does force from free energy mean?
It is an average driving force inferred from how free energy changes along a selected coordinate. The calculation describes the tendency to move toward lower free energy. It is most useful when the path and free energy change refer to the same physical segment.
2. Why does the formula have a negative sign?
The negative sign expresses motion toward lower free energy. If free energy falls as the coordinate increases, the calculated force is positive. If free energy rises along that coordinate, the calculated force is negative.
3. Can I enter kilojoules per mole?
Yes. Select the molar energy basis. The calculator converts your value to joules per particle by dividing by Avogadro’s constant. It then divides by the selected displacement to report force.
4. What displacement should I use?
Use the distance covered by the same process that produced the free energy change. For a curved energy profile, choose a short interval. Smaller intervals usually provide a better local approximation.
5. Is the result an instantaneous force?
Usually no. This calculator reports average force across a finite path segment. An instantaneous force needs the derivative of free energy with respect to position, written as negative dG divided by dx.
6. What does a positive force result mean?
It means force points in the positive coordinate direction that you selected. It does not automatically mean the force is upward, rightward, or forward. Your chosen coordinate convention defines the physical direction.
7. Can I use electronvolts?
Yes. Select eV as the energy unit. Use the single-system basis for energy per particle or modeled system. Use the molar basis only when your value genuinely represents electronvolts per mole.
8. Why choose pico newtons?
Pico newtons are practical for molecular and biological forces. They keep small values readable without changing the underlying force. One pico newton equals one trillionth of a newton.
9. Does temperature appear in the formula?
Not directly. Temperature is already included when the free energy value was determined. The calculator assumes your stated free energy change applies to the conditions of interest.
10. Can friction or drag change real motion?
Yes. Friction, viscous drag, thermal fluctuations, and constraints can affect measured motion. The result represents a thermodynamic driving force, not a complete dynamic model of every resistance.
11. When should I calculate several segments?
Use several segments when free energy changes nonlinearly with position. Calculate each short interval separately. Comparing the results shows how the driving force changes across the full path.