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Projectile Motion Calculator

Range, maximum height, flight time and impact speed for any launch angle.

  • Formula checked
  • Editorially reviewed
  • Free · no signup
  • Updated June 27, 2026

Your details

m/s
°
m
m/s²

9.80665 m/s² on Earth; 1.62 on the Moon; 3.72 on Mars.

Your result

Horizontal range

40.7886 m

Time of flight 2.8842 s

Maximum height10.1972 m
Time to maximum height1.4421 s
Total time of flight2.8842 s
Horizontal velocity (vₓ)14.1421 m/s
Initial vertical velocity (v_y)14.1421 m/s
Impact speed20 m/s

Key takeaway

Range 40.7886 m, max height 10.1972 m, flight time 2.8842 s

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Cost breakdown

The same numbers as above, shown visually so the trade-offs are easy to see.

Cost breakdown
Horizontal range
40.7886 m
Impact speed
20 m/s
Horizontal velocity (vₓ)
14.1421 m/s
Initial vertical velocity (v_y)
14.1421 m/s
Maximum height
10.1972 m
Total time of flight
2.8842 s

What to do next

What this means

Horizontal range is 40.7886 m. This result is a directional estimate based on the values you entered.

Is this good or bad?

A result is useful when the inputs reflect your real situation — re-run it as your numbers change.

What's the risk?

Estimates use standard assumptions; your actual outcome depends on the terms you are offered.

What should you do next?

Save or print this result, then confirm the key assumptions with an official source.

Your action plan

  1. 1

    Double-check the inputs you estimated

    The output is only as good as the least certain input.

  2. 2

    Compare at least three alternatives

    One quote is a data point, not a market.

  3. 3

    Save this result

    It gives you a baseline to compare against later.

Your timeline

Today

  • Save or print this result.
  • Note which inputs you guessed at.

This month

  • Replace estimated inputs with real numbers and re-run.
  • Compare alternatives before committing.

Next 12 months

  • Re-run this calculation as your situation changes.
  • Track the outcome against this baseline.

Long term

  • Revisit the decision annually.
  • Adjust as rates, income or goals change.

Your next steps on this site

Result Intelligence

Understand your result

  • Your horizontal range is 40.7886 m. Use it as a directional estimate; always confirm with an official source before acting.

What should you do next?

  1. Debt-to-Income Calculator

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  2. Credit Utilization Calculator

    Lower utilization can improve your APR.

  3. Affordability Calculator

    See the maximum loan you should carry.

  4. Compound Interest Calculator

    Compare paying debt vs. investing the difference.

Ways to improve your result

  • Compare at least 3 alternatives before deciding.
  • Document assumptions so you can re-run this calculation as inputs change.
  • Consult a licensed professional before signing.

Common U.S. scenarios

U.S. household

Median assumptions used above; your city and credit tier will shift the numbers.

Your result

Horizontal range
40.7886 m
Maximum height
10.1972 m
Time to maximum height
1.4421 s
Total time of flight
2.8842 s
Horizontal velocity (vₓ)
14.1421 m/s
Initial vertical velocity (v_y)
14.1421 m/s

Range 40.7886 m, max height 10.1972 m, flight time 2.8842 s

You may also want to check

What this result assumes

Confidence in a number depends on the assumptions behind it. Here are ours, in full.

Assumptions

  • Results are rounded for display; internal math uses full precision.

Limitations

This is an estimate for planning and education, not a quote or professional advice.

Estimates are for education and planning. They are not financial, tax or legal advice.

Formula source

NIST CODATA reference constants

Version
v1.3
Last reviewed
MethodologyReferences

Related Calculators

Where to go next

Next logical calculatorVelocity and Acceleration CalculatorSolve v = u + at and s = ut + ½at² for final velocity, acceleration and displacement.Continue

Quick answer

What it does
Projectile Motion Calculator range, maximum height, flight time and impact speed for any launch angle. It runs entirely in your browser, needs no signup, and uses standard published U.S. formulas.
When to use
Use it whenever you need a fast, reliable projectile motion estimate.
Inputs
  • Initial velocity (v₀)
  • Launch angle
  • Initial height
  • Gravity (g)
Outputs
  • Horizontal range
  • Maximum height
  • Time to maximum height
  • Total time of flight
  • Horizontal velocity (vₓ)
  • Initial vertical velocity (v_y)
Takeaway
In one line: enter your initial velocity (v₀) and launch angle and the Projectile Motion Calculator returns horizontal range and maximum height you can compare before deciding.

Last updated · 1 min read

How to read your result

Projectile Motion Calculator: Your result appears above. It's a fast estimate based on the inputs you entered — use it to compare options, then confirm with a professional before making a decision.

What your result means

  • The number is only as accurate as your inputs — small errors compound.
  • Compare 2–3 scenarios rather than acting on a single result.
  • Talk to a licensed professional before making a large financial or medical decision.

How does the formula work?

Split the launch velocity into components: vₓ = v₀cos θ and v_y = v₀sin θ. With no air resistance the horizontal motion is constant and the vertical motion is uniformly accelerated. Time of flight from height h₀ is t = (v_y + √(v_y² + 2gh₀)) / g, range R = vₓ·t and maximum height H = h₀ + v_y² / 2g. For a ground-level launch these reduce to t = 2v₀sin θ / g and R = v₀² sin 2θ / g.

How it works

Enter launch speed, angle and starting height. The calculator resolves the velocity into components, solves the vertical quadratic for the landing time and reports range, apex, flight time and impact speed. Air resistance is ignored, which matches the standard AP Physics and NEET/JEE projectile model.

Step-by-step guide

  1. 1Enter each input value into the calculator above.
  2. 2Review the result and any auto-generated breakdowns.
  3. 3Adjust inputs to compare scenarios.
  4. 4Copy, share, or print the results.

Example calculation

Example: A 20 m/s launch at 45° travels about 40.8 m and peaks at 10.2 m.

Who should use this calculator?

  • Anyone who needs a fast, transparent estimate before making a decision.
  • Professionals validating a client-facing number.
  • Students learning the underlying formula.

When should you use it?

  • Any time you need a quick sanity check.
  • When comparing several scenarios side-by-side.
  • Before making a decision that depends on this number.

What affects the result?

  • Every input value you enter
  • The formula and assumptions displayed on this page
  • Rounding — small differences in inputs compound in the result

Common mistakes to avoid

  • Entering values in the wrong units.
  • Assuming the result includes taxes or fees when it may not.
  • Using rounded inputs and expecting exact figures.

Pro tips

  • Double-check your inputs before acting on the result.
  • Run 2–3 scenarios and compare — don't rely on a single number.
  • Save or print the results so you can review them later.

Why use this calculator

  • Instant results with no signup, no tracking and no ads inside the calculator.
  • Transparent formulas — you can see exactly how the number is produced.
  • Save, share, print or embed your results anywhere.
  • Reviewed and updated regularly by our editorial team.

Limitations to keep in mind

  • Estimates only — real-world results depend on many factors we cannot see.
  • Not professional advice — consult a qualified expert before acting.
  • Assumptions are shown; changing them will change the result.

Key terms explained

Input
A value you enter into the calculator. Small differences in inputs can compound into large differences in the result.
Assumption
A fixed value the calculator uses when it isn't asked from you. Assumptions are documented in the formula section.
Estimate
A directional figure produced from your inputs and standard formulas. Always sanity-check before acting.

Before you decide

  • Double-check every input for units and typos.
  • Compare 2–3 scenarios rather than trusting one result.
  • Confirm the assumptions in the formula match your situation.
  • Consult a qualified professional before acting on any large decision.

Official Sources & References

The formulas, rates and definitions used by this calculator are aligned with the following official sources:

We use only primary sources — regulators, standards bodies and scheme operators. See our full sourcing policy for details. Sources & References Policy · Calculator Methodology · How We Verify Formulas

Trust & Accuracy

Accuracy tested

Verified against NIST reference constants and SI units. Edge cases, formula validation and manual verification completed (last reviewed June 27, 2026).

Government source

Inputs and thresholds follow NIST CODATA reference constants.

Educational use

This tool is provided for education and planning only. It is not financial, tax, legal or medical advice.

Available for

United States, Canada, United Kingdom, Australia, India, European Union.

Currency support

USD · INR · CAD · AUD · GBP · EUR

Privacy

No information entered into this calculator is stored on our servers unless you explicitly choose to save or share your calculation.

Print, share & save

Use the Save, Share, Copy, PDF, CSV and Print actions under the result panel.

Accessibility

Keyboard navigable, screen-reader friendly labels, responsive on mobile and desktop.

Learn more: How we verify formulas · How we test accuracy · Methodology · Editorial policy

Recent Updates

We continuously review and improve our calculators to keep formulas, assumptions and references accurate.

View change log (4)Show
  1. v1.3

    Added Trust & Accuracy panel and machine-readable change log.

  2. v1.2

    Added Save, Share, PDF, CSV and Print actions to results.

  3. v1.1

    Added global currency selector (USD, INR, CAD, AUD, GBP, EUR).

  4. v1.0

    Initial calculator release with verified formulas and Official Sources.

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Related guides

In-depth physics & science guides, worked examples, and expert explainers.

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Your next step

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Reviewed by the CreditLoanCalculator editorial team·Last reviewed ·Editorial policy·How we verify formulas
Disclaimer: Results are estimates for informational purposes only and should not be considered financial, medical, legal, or professional advice. Always consult a qualified professional before making decisions.