Newton Forward Difference

Summary

Enter equally spaced x,y data points to build a forward difference table and interpolate values at any x.

How it works

1. Enter your data points as x,y pairs — x values must be equally spaced.
2. The tool computes successive forward differences: Δy, Δ²y, Δ³y, etc.
3. The full difference table is displayed with every computed value.
4. Enter a target x value to interpolate; the tool calculates p = (x - x₀) / h.
5. The Newton forward interpolation formula sums the difference terms to produce the result.

Use cases

• Estimate intermediate values from experimental data tables.
• Solve numerical analysis homework involving finite differences.
• Verify hand-calculated difference tables quickly.
• Interpolate population, temperature, or sensor readings at off-grid points.
• Understand how the Newton forward formula accumulates difference terms.

Frequently Asked Questions